Question

In ΔUVW, the measure of ∠W=90°, the measure of ∠V=72°, and VW = 6.1 feet. Find the length of UV to the nearest foot.

Answer 1

The length of UV is 19.7 ft.

Solution:

The given $\triangle UVW$ is a right triangle because W is 90 degrees. VW is adjacent to V and UV is the hypotenuse. Adjacent any hypotenuse use the cosine function. 

Refer the image attached below for the image of the triangle.

$cos\theta=\frac{adj}{hyp}$

plug in known values

$cos(72\°)=\frac{6.1}{x}\rightarrow(1)$

The value of cos(72°) is 0.309

On substituting the above value in (1) we get,

$\Rightarrow0.309=\frac{6.1}{x}\rightarrow x=\frac{6.1}{0.309}\rightarrow x=19.7411003236\approx x=19.7$

Therefore, the required measure is 19.7 ft.