Mathematics, 15.10.2020 07:01 drobledo9

1 A student whose eye level is 182 cm from the ground observed the top of their house at an angle of elevation of 32 at point A She walked for 20m towards the house along a
straight road to a point B where she observed the top of the building again at an angle of
elevation of 40 Calculate corect to 2 decimal places the-
(a) Distance of A from the bouse
(3mks)
(b) The height of the house
(2mks)
2. Given that an X=5/ 12 find the value of the following without using mathematical tables or
calculator
(a) Cos x
(2mks)
(b) Sin (90-x)
2mics)

Answers: 1

Show answers

Answers

Answer from: TamB01

Question 1)

$\text{ Distance from A to the house is approximately 78.34 meters}\\\text{The height of the house is approximately 50.77 meters}$

Question 2)

$\text{ Part A) \cos(x)=\frac{12}{13}} \\ \text{ Part B) \sin(90-x)=\frac{12}{13} }$ $\text{ Part A) }\\\cos(x)=\frac{12}{13}\\\\\text{ Part B)}\\\sin(90-x)=\frac{12}{13}$

Step-by-step explanation:

Question 1)

Please first reference below for the image.

Also recall the basic trigonometric functions with SohCahToa.

Part 1)

In order to find the distance, we will need to find the value of . However, to do so, we must find the value of first.

First, we will need to find BM. We can use the smaller triangle. BM is opposite of the smaller triangle, and we already know that the hypotenuse is 20 meters. So, we can use sine:

$\sin(A)=\frac{\text{opp}}{\text{hyp}}$

Substitute 32° for A and 20 for the hypotenuse. Our BM is our opposite, so substitute BM for opposite. This yields:

$\sin(32)=\frac{BM}{20}$

Solve for BM. Multiply both sides by 20:

$BM=20\sin(32)$

Don't approximate just yet. In order to make our answer to most precise, we will approximate at the very end.

So, BM is 20sin(32) meters. BM of the smaller triangle is the same as BM of the larger triangle, so BM of the larger triangle is also 20sin(32). Now, we can find the value of . However, we will first need to find the value of $\angle MBT$ . To do so, notice that $\angle ABM, \angle MBT, \text{ and } 40\textdegree$ form a straight angle. Therefore:

$\angle ABM+\angle MBT+40^\circ=180$

Simplify:

$\angle ABM+\angle MBT=140$

So, we will need to find $\angle ABM$ , which is $\angle B$ of the smaller triangle. So, we can use the trig functions again. Since we now know BM, we can use cosine. So:

$\cos(B)=\frac{\text{adj}}{\text{opp}}$

Substitute 20sin(32) for the adjacent and 20 for the opposite. So:

$\cos(B)=\frac{20\sin(32)}{20}$

To solve for B, take the inverse cosine of both sides. Evaluate:

$B=\cos^{-1}(\frac{20\sin(32)}{20})=58^\circ$

Therefore, we can substitute 58 for $\angle ABM$ and solve. This yields:

$58+\angle MBT=140\\\Rightarrow\angle MBT=82^\circ$

So, we can now find c. We know BM and that $\angle B$ (of the larger triangle) is 82°. To find c, then, we will use cosine. So:

$\cos(B)=\frac{\text{adj}}{\text{hyp}}$

Substitute 82 for B, 20sin(32) for the adjacent BM, and c for the hypotenuse. So:

$\cos(82)=\frac{20\sin(32)}{c}$

Solve for c by cross-multiplying:

$c=\frac{20\sin(32)}{\cos(82)}$

Now, finally, we can solve for . We know (the hypotenuse) and we want to find . We also have an angle of 40°. So, we can use cosine:

$\cos(40)=\frac{x}{c}$

Multiply both sides by :

$x=c\cos(40)$

Substitute :

$x=\frac{20\sin(32)\cos(40)}{\cos(82)}$

Approximate:

$x\approx58.34\text{ meters}$

However, this is only . The distance from the house is x+20 . Therefore, the distance from the house is:

$d\approx58.34+20\approx78.34\text{ meters}$

Part 2)

We want to find the height h. Since we already determined , we can use it to find . We will use the sine function this time:

$\sin(40)=\frac{h}{c}\\\Rightarrow h=c\sin(40)\\\Rightarrow h=\frac{20\sin(32)\sin(40)}{\cos(82)}\\\Rightarrow h\approx48.95$

However, we will still need to add the eye level of 182 centimeters or 1.82 meters. So:

$h\approx48.95+1.82\approx50.77\text{ meters}$

The height of the house is approximately 50.77 meters.

Question 2)

We know that: $\tan(x)=\frac{5}{12}$

Remember that tangent is the opposite side over the adjacent side. So, let's find the hypotenuse. We can us the Pythagorean Theorem:

a^2+b^2=c^2

Substitute 5 for a and 12 for b. Solve for c:

$c^2=(5)^2+(12)^2\\\Rightarrow c^2=25+144\\\Rightarrow c=\sqrt{169}=13$

So, our hypotenuse is 13, our adjacent is 12, and our opposite is 5. We can now solve for the others:

$\cos(x)=\frac{\text{adj}}{\text{hyp}}\\\Rightarrow\cos(x)=\frac{12}{13}$

$\sin(90-x)=\cos(x)\\\text{Note: This is a cofunction identity}\\\Rightarrow\sin(90-x)=\frac{12}{13}$

Note: The document I found said $\sin^2(90-x)$ . Anyways, it will just be: $\sin^2(90-x)=\frac{144}{169}$

1 A student whose eye level is 182 cm from the ground observed the top of their house at

an angle o

Answer from: Quest

answer: i believe c. is the answer sorry if i am wrong

step-by-step explanation:

Ineed on this ! and you . i set this for 45 points!

Answer from: Quest

121 pints. they had 176 and drank 55

Another question on Mathematics

Mathematics, 21.06.2019 14:30

Simonne used the following steps to simplify the given expression. 12 - 3(-2x + 4) step 1: 12 + (–3)·(–2x) + (–3)·(4) step 2: 12 + 6x + (–12) step 3: 12 + (–12) + 6x step 4: 0 + 6x step 5: 6x what property of real numbers was used to transition from step 3 to step 4? a. identity property of addition b. inverse property of addition c. associative property of addition d. commutative property of addition

Answers: 1

Answer

Mathematics, 21.06.2019 15:10

Drag each sequence of transformations to the correct location on the table. classify the sequences of transformations based on whether or not they prove the congruency of the shapes by mapping shape i onto shape ii. plz i'll rate u 5 stars need this done for a mastery test

Answers: 1

Answer

Mathematics, 21.06.2019 16:30

Write each fraction as an equivalent fraction with a denominator of 120then write the original fractions in order from samllest to largest

Answers: 3

Answer

Mathematics, 21.06.2019 21:00

An account with a $250 balance accrues 2% annually. if no deposits or withdrawals are made, which graph can be used to determine approximately how many years will it take for the balance to be $282? it's e2020 ni️️as

Answers: 1

Answer

You know the right answer?

1 A student whose eye level is 182 cm from the ground observed the top of their house at an angle o...

Questions