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1 year ago

Solve the right triangle. Round to the nearest degree and nearest tenth of a unit. What is the right angleV?

Mathematics

1 answer:

N76 [4]1 year ago

4 0

Answer:

m∠V ≈ 61°

Step-by-step explanation:

The hypotenuse and the side opposite the angle of interest are given. The relevant trig relation is ...

Sin = Opposite/Hypotenuse

sin(V) = XW/XV = 7/8

The inverse sine function is used to find the angle:

V = arcsin(7/8) ≈ 61°

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Add all of these values up and set it all equal to $78$ .

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Now, simplify.

$4x+6=78$

Subtract $6$ on both sides.

$\begin{aligned}4x+6-6&=78-6\\4x&=72\end{aligned}$

Divide both sides by $4$ .

$\begin{aligned}\frac{4x}{4}&=\frac{72}{4}\\x&=\boxed{18}\end{aligned}$

Since Louise's score is $x$ , the answer is $18$ .

<h3>Double-checking</h3>

To verify our answer, add the point totals $18$ , $19$ , $20$ , and $21$ .

This equals $78$ , so we can be sure the answer is correct.

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