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kupik [55]
2 years ago
11

Please help quick!! Given ΔΡHS & ΔCNF, find the values of x, y, and z.

Mathematics
1 answer:
valkas [14]2 years ago
3 0

Answer:

x=24, y=10, z=17

Step-by-step explanation:

We know that \Delta PHS\cong\Delta CNF.

Then by CPCTC, ∠P≅∠C, ∠H≅∠N, and ∠S≅∠F.

Therefore, let’s solve for each of the angle relations.

∠P≅∠C:

We know that ∠P is 36°. ∠C is (4z-32)°. Therefore:

36=4z-32

Solve for z:

\begin{aligned}36&=4z-32\;\;\; \text{Add 32 to both sides}\\68&=4z\;\;\;\;\;\;\;\;\;\;\;\text{Divide both sides by 4}\\17&=z\end{aligned}

So, the value of z is 17.

∠H≅∠N

∠H is (6x-29) and ∠N is 115. So:

6x-29=115

Solve for x:

\begin{aligned} 6x-29&=115\;\;\;\;\;\;\text{Add 29 to both sides}\\6x&=144\;\;\;\;\;\;\text{Divide both sides by 4}\\\ x&=24\end{aligned}

Therefore, the value of x is 24.  

∠S≅∠F

We will need to find ∠S.

We already know that ∠P is 36.

∠H will be (6x-29). Substitute 24 for x to acquire: (6(24)-29)=144-29=115.

A triangle always totals 180°. Therefore, 115+36+∠S=180 or 151+∠S=180.

Therefore, ∠S=29.

∠F is (3y-1). So:

29=3y-1

Solve for y:

\begin{aligned} 29&=3y-1\;\;\;\;\;\text{Add 1 to both sides}\\ 30&=3y\;\;\;\;\;\;\;\;\;\;\text{Divide both sides by 3}\\ 10&=y\end{aligned}

Therefore, the value of y is 10.

So, x=24, y=10, and z=17.

And we are done!

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Calculate the angle of depression, x, if the boat is 850 ft. away from the lighthouse and the lighthouse is 250 ft. high. Round
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Firstly , we can draw diagram

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x=16.38

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angle of depression is 16.38 degree........Answer

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3 years ago
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LUCKY_DIMON [66]

Answer:

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Step-by-step explanation:

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3 years ago
Can someone please help me with both of these questions. Thanks so much.
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(1.) Part A
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3 years ago
Read 2 more answers
2. When do you use trig functions?
klasskru [66]

Hey there!

2. Your answer is A. Given a right triangle and you know one side and one angle.

It is important that these trig functions we're talking about are used for right triangles only. They don't work on other triangles. You also need at least one side and at least one angle to be able to do any of them.

3. Your answer is D. opposite/adjacent.

Tangent is the side opposite the angle over/divided by the side adjacent to the angle. There's a way to remember this, which is question 5...

5. Your answer is D. SOH-CAH-TOA.

A lot of my teachers in the past have given me this awful joke to help remember this. I'm sorry to put you through the bad joke but it does help to remember.

What did the teacher do when he stubbed his toe?

He soh-cah-toa (soaked the toe).

Sorry again.

S stands for sine, C stands for cosine, T stands for tangent, O stands for opposite (side), A stands for adjacent (side), and H stands for hypotenuse.

Hope this helps!

3 0
3 years ago
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