Looking at the top of tower A and base of tower B from points C and D, we find that ∠ACD = 60°, ∠ADC = 75° and ∠ADB = 30°. Let the distance between points C and D be 100. Find the height AB of the tower.
Picture attached for the problem. Please show your work too. Thanks!
Answers
Answer:
[tex]\text{Exact: }AB=25\sqrt{6},\\\text{Rounded: }AB\approx 61.24[/tex]
Step-by-step explanation:
We can use the Law of Sines to find segment AD, which happens to be a leg of [tex]\triangle ACD[/tex] and the hypotenuse of [tex]\triangle ADB[/tex].
The Law of Sines states that the ratio of any angle of a triangle and its opposite side is maintained through the triangle:
[tex]\frac{a}{\sin \alpha}=\frac{b}{\sin \beta}=\frac{c}{\sin \gamma}[/tex]
Since we're given the length of CD, we want to find the measure of the angle opposite to CD, which is [tex]\angle CAD[/tex]. The sum of the interior angles in a triangle is equal to 180 degrees. Thus, we have:
[tex]\angle CAD+\angle ACD+\angle CDA=180^{\circ},\\\angle CAD+60^{\circ}+75^{\circ}=180^{\circ},\\\angle CAD=180^{\circ}-75^{\circ}-60^{\circ},\\\angle CAD=45^{\circ}[/tex]
Now use this value in the Law of Sines to find AD:
[tex]\frac{AD}{\sin 60^{\circ}}=\frac{100}{\sin 45^{\circ}},\\\\AD=\sin 60^{\circ}\cdot \frac{100}{\sin 45^{\circ}}[/tex]
Recall that [tex]\sin 45^{\circ}=\frac{\sqrt{2}}{2}[/tex] and [tex]\sin 60^{\circ}=\frac{\sqrt{3}}{2}[/tex]:
[tex]AD=\frac{\frac{\sqrt{3}}{2}\cdot 100}{\frac{\sqrt{2}}{2}},\\\\AD=\frac{50\sqrt{3}}{\frac{\sqrt{2}}{2}},\\\\AD=50\sqrt{3}\cdot \frac{2}{\sqrt{2}},\\\\AD=\frac{100\sqrt{3}}{\sqrt{2}}\cdot\frac{ \sqrt{2}}{\sqrt{2}}=\frac{100\sqrt{6}}{2}={50\sqrt{6}}[/tex]
Now that we have the length of AD, we can find the length of AB. The right triangle [tex]\triangle ADB[/tex] is a 30-60-90 triangle. In all 30-60-90 triangles, the side lengths are in the ratio [tex]x:x\sqrt{3}:2x[/tex], where [tex]x[/tex] is the side opposite to the 30 degree angle and [tex]2x[/tex] is the length of the hypotenuse.
Since AD is the hypotenuse, it must represent [tex]2x[/tex] in this ratio and since AB is the side opposite to the 30 degree angle, it must represent [tex]x[/tex] in this ratio (Derive from basic trig for a right triangle and [tex]\sin 30^{\circ}=\frac{1}{2}[/tex]).
Therefore, AB must be exactly half of AD:
[tex]AB=\frac{1}{2}AD,\\AB=\frac{1}{2}\cdot 50\sqrt{6},\\AB=\frac{50\sqrt{6}}{2}=\boxed{25\sqrt{6}}\approx 61.24[/tex]
Answer:
[tex] \displaystyle 25 \sqrt{6} [/tex]
Step-by-step explanation:
the triangle ∆ABD is a special right angle triangle of which we want to figure out length of its shorter leg (AB).
to do so we need to find the length of AD (the hypotenuse). With the help of ∆ADC it can be done. so recall law of sin
[tex] \boxed{ \displaystyle \frac{ \alpha }{ \sin( \alpha ) } = \frac{ \beta }{ \sin( \beta ) } = \frac{ c}{ \sin( \gamma ) } }[/tex]
we'll ignore B/sinB as our work will be done using the first two
step-1: assign variables:
[tex] \sin( \gamma ) = \sin( {60}^{ \circ} ) [/tex][tex]c=AD[/tex][tex] \rm \sin( \alpha ) = \sin( {180}^{ \circ} - ({60}^{ \circ} + {75}^{ \circ} )) = \sin( {45}^{ \circ} ) [/tex][tex]a=100[/tex]step-2: substitute
[tex] \displaystyle \frac{100}{ \sin( {45}^{ \circ} )} = \frac{AD }{ \sin( {60}^{ \circ} )} [/tex]
recall unit circle therefore:
[tex] \displaystyle \frac{100}{ \dfrac{ \sqrt{2} }{2} } = \frac{AD }{ \dfrac{ \sqrt{3} }{2} } [/tex]
simplify:
[tex]AD = 50 \sqrt{6} [/tex]
since ∆ABD is a 30-60-90 right angle triangle of which the hypotenuse is twice as much as the shorter leg thus:
[tex] \displaystyle AB = \frac{50 \sqrt{6} }{2}[/tex]
simplify division:
[tex] \displaystyle AB = \boxed{25 \sqrt{6} }[/tex]
and we're done!
Related Questions
PLEASE HELP ASAP!!!!!Sunny earns $22.75 per week delivering newspapers. He worked as a delivery boy for 3 weeks. He also earned $32.75 last
month doing chores around the house. He spent $14.25 of his total earnings to download music on his mobile device. Sunny put
of the remaining money in his savings account. Sunny used the following steps to find the total money he put in his savings
5
account:
Step 1: [($22.75 + 3) + $32.75 - $14.25)
5
Step 2: [$44.25)
Step 3: $11.0625
In which step did Sunny first make an error? Use words to explain how Sunny can correct his error.
Answers
Answer:
error in step one
Step-by-step explanation:
Sunny earns $22.75 per week delivering. delivery boy for 3 weeks.
That means $22.75 x 3 not $22.75 + 3
He can correct his mistake by doing this:
Step 1: [($22.75 * 3) + $32.75 - $14.25] * 1/ 5
Step 2: [$86.75] *1/5
Step 3: $17.35
Answer:
putting this so the other might be brainliest!
Step-by-step explanation:
also, be extremely careful, you put the link for your school and your teachers name on the top of the photo! sorry if i sound creepy lol, but yeah :)
If onee moderator was typing why this website is bad every 20 minutes and the other was trying to update this site every 30 minutes by what time will the one updating the site find out about the insults
Answers
Answer: 60 minutes or 1 hour.
Step-by-step explanation:
Since one moderator was typing every 20 minutes while the other moderator was typing every 30 minutes, then the time the other one will find about the insult simply means that we should find the lowest common multiple of 20 and 30. This will be:
20 = 20, 40, 60, 80, 100, ..
30 = 30, 60, 90, 120 .....
Here, we can see that the lowest common multiple is 60. Therefore, the other one will find about the insults in 60 minutes.
Complete each statement. If the triangles cannot be shown to be congruent from the information given, leave the triangles name blank and write Cannot Be Determined (CNBD) in the spot for rule. ∆SAT ≅ ∆_____ By _____
Answers
Answer:
The answer is "[tex]\bold{\Delta LAW \cong \Delta WKL}[/tex]. By applying the ASA congruence postulate rule".
Step-by-step explanation:
[tex]\Delta LAW\ and\ \Delta WKL\\\\AW\perp WL\ and \ WL\perp KL\\\\\angle AWL = \angle WLK .......[each \ 90^{\circ}]\\\\WL=WL.......\ [Reflexive \ property]\\\\\angle ALW = \angle KWL........\text{give in picture}\\\\[/tex]
[tex]\therefore,[/tex] by ASA postulate of congruence
[tex]\Delta LAW \cong \Delta WKL\\\\[/tex]
The ASA postulate states that when two angles on the included side with one triangle were congruent to two angles on the included side of the second triangle, then the triangles are said to have been congruent.
Write an equation, in slope-intercept form, of the line that passes through the given point and satisfies the given condition. (-1, -4); perpendicular to y=2x+5
Answers
Answer:
y = -1/2x - 9/2
Step-by-step explanation:
In right A ABC, B is a right angle and sin _ C= x.
sin A=
V1 – *2
22
Ох,
O2 - 1
+1
Answers
Answer:
Step-by-step explanation:
please help me with this also if your good at geometry please dm me I need serious help!!
Answers
Answer:
0.92
Step-by-step explanation:
cosine = adjacent/ hypotenuse
cosine of t = 12/ 13
cos t= 0.92308
Write a fraction setting the vertical length of the larger triangle over its horizontal length. What does this fraction represent?
Answers
Answer:
[tex]Ratio = \frac{2}{3}[/tex]
Step-by-step explanation:
Given
See attachment
Required
Vertical length / Horizontal length
From the attachment, we have:
[tex]y = 4\ units[/tex] --- the vertical length of the larger triangle
and
[tex]x = 6\ units[/tex] --- the horizontal length of the larger triangle
So, the ratio is:
[tex]Ratio = \frac{y}{x}[/tex]
[tex]Ratio = \frac{4\ units}{6\ units}[/tex]
[tex]Ratio = \frac{4}{6}[/tex]
Divide by 2
[tex]Ratio = \frac{2}{3}[/tex]
Find the length of the segment indicated. Round to the nearest tenth if necessary.
Answers
Answer:
x=5
Step-by-step explanation:
x is the length of the line segment from the center to the boderline of circle. So x=5
Please help me ASAP!! Please write answer in inequalities form! Thanks so much! :)
Answers
Answer:
.5 < 2 - sqrt(2) < .6
Step-by-step explanation:
sqrt() is larger than 1.4 and less than 1.5
2 - sqrt(2) 2 -1.4 = .6
2 - sqrt (2) 2 - 1.5 = .5
.5 < 2 - sqrt(2) < .6
[tex]1.4 < \sqrt{2} <1.5 \\ - 1.5 < - \sqrt{2} < - 1.4 \\ 2 - 1.5 < 2 - \sqrt{2} < 2 - 1.4 \\ 0.5 < 2 - \sqrt{2 } < 0.6[/tex]
Which sequence is arithmetic? Check all that apply.
•0, 8, 16, 24
•7, 12, 17, 22
•6, 12, 24, 48
•8, 14, 20, 26
•11, 18, 23, 30
•12, 17, 22, 29
•15, 30, 60, 120
Answers
Answer:
Sequences 1,2, and 4 are arithmetic.
Step-by-step explanation:
Each term in sequence 1 gets added by 8.
Each term in sequence 2 gets added by 5.
Each term in sequence 4 gets added by 6.
Pls what is the formula for finding the base and the height of a triangular pyramid.
Answers
Answer:
Take the Cubits and multiply
Step-by-step explanation:
This is a problem i had so just fill it in to your numbers etc.
A= 43.3 cubits squared
SA= the base of A +1/2 (p x slant h)
SA= 43.3 cubits squared + 1/2 (30 x 14 cubits)
To sum it up u can message me ur numbers and ill help
Which of the following shapes is the cross-section for a cone?
O A. Pentagon
O B. Square
O C. Triangle
O D. Circle
Answers
Answer:
The choose (D)
D. Circle
I hope I helped you^_^
The required cross-section for a cone is a circle. Option D is correct.
What is a conic section?A conic section is a geometric shape that is obtained by intersecting a cone with a plane. Conic sections include circles, ellipses, parabolas, and hyperbolas.
The type of conic section that is formed depends on the angle of the plane relative to the axis of the cone, as well as the distance of the plane from the vertex of the cone.
Here,
The cross-section of a cone is a circle.
A cross-section is a shape that you get when you slice a 3D object with a plane. If you slice a cone parallel to its base, you get a circle as the cross-section.
Therefore, the correct answer is option D.
Learn more about the conic section here;
https://brainly.com/question/28991363
#SPJ7
If the sum of seven odd consecutive numbers is 231, find the middle number.
Answers
Answer:
33
Step-by-step explanation:
(1+x) + (3+x) + (5+x) + (7+x) + (9+x) + (11+x) + (13+x) = 231
7x + 49 = 231
7x = 231 - 49
7x = 182
x = 182/7
x = 26
To find the middle number;
7 + x
= 7+26
= 33
I WILL GIVE BRAINLIEST IF TWO PEOPLE ANSWER! PLEASE PUT WHAT X IS, AND PLEASE PUT THE REASONS OF HOW YOU DID IT, FOR INSTANCE, SUBSTITUTION, OR ALTERNATE INTERIOR ANGLES
Answers
Answer:
14°
Step-by-step explanation:
4x + 32 + 64 = 180 => x = 14 (°)
Someone please help me!!!
Answers
Answer:
<2 = 75°
<3 = 75°
Step-by-step explanation:
<2 = <6
2x+15 = 45+x
or, 2x-x = 45-15
or, x = 30
so, <2 = 30×2+15 = 75
<6 = 45+30 = 75
Answered by GAUTHMATH
Brianna's Bakery offers 3 flavors of bagels. Customers can choose from plain, cinnamon, or blueberry bagels. Yesterday, a customer ordered 144 bagels for a company meeting. The order was for twice as many blueberry bagels as plain bagels and 3 times as many cinnamon bagels as blueberry bagels.
How many cinnamon bagels did the customer order
Answers
Answer:
96 darling
Step-by-step explanation:
youre gonna take all the times this was teice as mich as that
like this:blueberrybagel twice as much 2
than plain bagels 1
cinnamonbags 3 times as much than
blueberry bagels 2×3= 6+
=9
EACH portion contains144:9=16 bagels
blueberry ones16×2=32
plain ones16×1=16
cinnamon ones 3×32=96
Robi bought a toy car for $x. He sold it at a loss of 10%. Find the expression
for the selling price.
Answers
Step-by-step explanation:
loss amount'= loss% × C.P
=10/100 × x
=0.1 x
Again,
S.P = C.P - Loss amount
=$x - $0.1 x
=0.9 x
The expression for the selling price is:
0.9x
What is selling price and cost price and its formula?
Cost Price: The price paid for an item is referred to as its cost price (C.P.). The price at which an item is purchased is referred to as its selling price (S.P.).
Profit or Gain: The seller is considered to have profit or gain if SP exceeds CP.
Solution:
Given, loss percent is = 10%
cost price of the toy car is = $x
Therefore the loss amount is: loss% × C.P
= 10/100 × cost price
= 0.1x
Now, for the selling price expression:
selling price (SP) = Cost price ₋ Loss amount
= $x ₋ $0.1x
= 0.9x
Hence we get the desired expression for the selling price as 0.9x.
Learn more about "selling price questions" here-
brainly.com/question/1153322
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if the radius of a sphere is7 cm find its volume
Answers
Answer:
1437.33 cm square
Step-by-step explanation:
Now we will use the frmula to et the volume of a sphere
volume of sphere is
4÷3pi r cube
where r is the radius of the sphere
Find an explicit rule for the nth term of the sequence.
The second and fifth terms of a geometric sequence are 20 and 1280, respectively.
Answers
Step-by-step explanation:
in a geometric sequence there is a constant factor x that is multiplied with every previous term to create the next one.
a2 = 20
a5 = 1280 = a2×x×x×x = a2×x³ = 20x³
64 = x³
x = 4
=> a1 = 5
therefore
an = an-1×4 =
[tex]a1 \times {4}^{n - 1} [/tex]
n > 1
Solve the simultaneous equation, will give out brainliest answer
a=bcd
a+b=cd
a+b+c=d
a+b+c+d=1
Answers
Answer:
a = 1/42, b = 1/7, c = 1/3 and d = 1/2
Step-by-step explanation:
a = bcd (1)
a + b = cd (2)
a + b + c = d (3)
a + b + c + d = 1 (4)
Substituting equation (3) into equation (4), we have
a + b + c = d (3)
a + b + c + d = 1 (4)
(a + b + c) + d = 1 (4)
d + d = 1 (5)
2d = 1
dividing through by 2, we have
d = 1/2
Taking equation (2) and equation (3), we have
a + b = cd (2)
a + b + c = d (3)
substituting equation (2) into equation (3), we have
a + b = cd (2)
(a + b) + c = d (3)
cd + c = d
Factorizing, we have
c(d + 1) = d
dividing through by d + 1, we have
c = d/(d + 1)
substituting d = 1/2 into the equation, we have
c = d/(d + 1)
c = 1/2 ÷ (1/2 + 1)
c = 1/2 ÷ 3/2
c = 1/2 × 2/3
c = 1/3
Taking equations (1) and (2), we have
a = bcd (1)
a + b = cd (2)
Substituting equation (1) into (2), we have
a = bcd (1)
a + b = cd (2)
bcd + b = cd (2)
Factorizing, we have
b(cd + 1) = cd
dividing through by (cd + 1), we have
b = cd/(cd + 1)
substituting the values of c and d into the equation,, we have
b = cd/(cd + 1)
b = 1/3 × 1/2/(1/3 × 1/2 + 1)
b = 1/6/(1/6 + 1)
b = 1/6 ÷ 7/6
b = 1/6 × 6/7
b = 1/7
Since a = bcd, substituting the values of b,c and d into the equation, we have
a = bcd
a = 1/7 × 1/3 × 1/2
a = 1/42
So, a = 1/42, b = 1/7, c = 1/3 and d = 1/2
Graph the solution to the following system of inequalities.
y-2x-9
y<2x+7
Answers
Answer:
Tb bight by icing I jb Yves j by by by navy by iffy i by by by
simplify 4x^2-3xy+2xy+9x^2
Answers
Answer:
13x^2 - xy
Step-by-step explanation:
4x^2-3xy+2xy+9x^2
=13x^2-xy
HELP ME PLS I NEEDA GET THIS RIGHT PLS PLS ITS PYTHAGOREAN THEOREM
Answers
2.8 mm
2mm^2=4mm
4mm+4mm = 8mm
square root of 8mm is 2sqrt2
2sqrt 2 is 2.8 mm
[tex]\frac{-3}{\sqrt{x} +3} +\frac{1}{2}[/tex]
Answers
[tex]\huge\bold\color{blue}{⁂Answer:}[/tex]
[tex]\bold{ - \frac{6 \sqrt{x} - x - 9 }{2(x - 9)} }[/tex]
#CarryOnLearning
[tex]\bold\color{red}{༄Fairy \: Elfꨄ︎}[/tex]
HELP PLS HELP MEEEEE IM FAILING PYTHAGOREAN THEOREM
Answers
7^2 + 6^2 = h^2
49 + 36 = h^2
85 = h^2
√85 = h
h = 9.21m
Answered by Gauthmath must click thanks and mark brainliest
A system of linear equations includes the line that is created by the equation y = x+ 3, graphed below, and the line through the points (3, 1) and (4, 3).
On a coordinate plane, a line goes through (0, 3) and (2, 5).
What is the solution to the system of equations?
(–1, 2)
(1, 3)
(8, 11)
(9, 12)
i really dont get this at all can someone help me and explain
Answers
Answer:
(8,11)
Step-by-step explanation:
1st line
y = x+ 3
We need to find the equation of the other line
We have two points (3, 1) and (4, 3)
Slope
m = (y2-y1)/(x2-x1)
= ( 3-1)/(4-3)
= 2/1 = 2
The slope intercept form is y = mx+b where m is the slope and b is the y intercept
y =2x+b
Using the point (4,3)
3 = 2(4)+b
3 = 8+b
3-8=b
-5 =b
y = 2x-5
We have 2 lines
y =x+3 and y = 2x-5
Setting them equal to each other
x+3 = 2x-5
Subtract x from each side
x+3-x = 2x-5-x
3 = x-5
Add 5 to each side
3+5 =x-5+5
8=x
Now we can find y
y =x+3
y = 8+3
y=11
Answer:
c (8,11)
Step-by-step explanation:
2-6=? need help please
Answers
The answer is -4
Step-by-step explanation:
2 - 6 = -4
Trong mặt phẳng tọa độ cho tam giác ABC biết các đỉnh A(-1,2), B(4,7) và trọng tâm tam giác G(3,2). Viết phương trinh đường thẳng d chứa đường cao đi qua A của tam giác ABC
Answers
It is believed that the average amount of money spent per U.S. household per week on food is about $99, with standard deviation $10. A random sample of 25 households in a certain affluent community yields a mean weekly food budget of $100. We want to test the hypothesis that the mean weekly food budget for all households in this community is higher than the national average. State the null and alternative hypotheses for this test, the test statistic and determine if the results significant at the 5% level.
Answers
Answer:
H0 : μ = 99
H1 : μ > 99
Z statistic = 0.5
Result is not significant at 5% level ;
Step-by-step explanation:
Given that :
σ = 10
μ = 99
Sample size, n = 25
H0 : μ = 99
H1 : μ > 99
The test statistic :
(xbar - μ) ÷ (σ/√(n))
Since the population standard deviation is known, we use the Z statistics.
Z = (100 - 99) ÷ (10/√(25))
Z = 1 / 2
Z = 0.5
The Z critical value at α = 0.05
Zcritical = 1.645
Zstatistic < Zcritical ; Hence, we fail to reject the H0.
Which expressions in the picture are equivalent to (v^-1)^1/9? Choose all answers that apply:
Answers
Answer:
All of them: A, B, and C
Step-by-step explanation:
Answer:
A, B, and C
Step-by-step explanation:
Recall the exponent property [tex](a^b)^c=a^{(b\cdot c)[/tex].
Therefore,
[tex](v^{-1})^{1/9}=(v^{1/9})^-1=v^{-1/9}[/tex]
In addition, fraction exponents can be written as radicals such that:
[tex]a^{b/c}=\sqrt[c]{a^b}[/tex]
Thus, [tex](\sqrt[9]{v})^{-1}=(v^{1/9})^{-1}=(v^{-1})^{1/9}[/tex].
Therefore, answer choices A, B, and C are correct.
