In ΔVWX, the measure of ∠X=90°, the measure of ∠W=20°, and XV = 58 feet. Find the length of VW to the nearest tenth of a foot.

Question

Mathematics

Cadence

27 December, 17:06

In ΔVWX, the measure of ∠X=90°, the measure of ∠W=20°, and XV = 58 feet. Find the length of VW to the nearest tenth of a foot.

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Answers (1)

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Coby · Answer 1

169.6

Step-by-step explanation:

We can use trig to find the missing side (sin specifically). sin (x) = opposite/hypotenuse. where x is the angle. VWX is 20 degrees. The side opposite to that angle is VX or 58. We dont know the hypotenuse. If we were to substitute values into sin (x) = opposite/hypotenuse, we would get sin (20) = 58/hypotenuse. sin (20) in the calculator is 0.342020143 ... so we can rewrite the equation as 0.342020143=58/hypotenuse. Lets call the hypotenuse h. If we multiply h on both sides, we can try to find what h is equal to. 0.342020143h=58. Now we can divide 0.342020143 on both sides to isolate h. h=169.58 ... or if we round it, we get 169.6