Question

In ΔTUV, the measure of ∠V=90°, the measure of ∠U=55°, and VT = 82 feet. Find the length of TU to the nearest tenth of a foot.

Answer 1

Given:

Given that TUV is a right triangle with measure of ∠V=90°

The measure of ∠U = 55°, and the length of VT is 82 feet.

We need to determine the length of TU.

Length of TU:

The length of TU can be determined using the trigonometric ratio.

Thus, we have;

$sin \ \theta=\frac{opp}{hyp}$

where $\theta=55^{\circ}$, opp = VT and hyp = TU

Thus, we have;

$sin \ 55^{\circ}=\frac{VT}{TU}$

Substituting the values, we have;

$sin \ 55^{\circ}=\frac{82}{TU}$

Simplifying, we have;

$TU=\frac{82}{sin \ 55^{\circ}}$

$TU=\frac{82}{0.819}$

$TU=100.1$

Thus, the length of TU is 100.1 feet.