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=(opp)/(hyp)`

where
`\theta=55^(\circ)`, opp = VT and hyp = TU

Thus, we have;

`sin \ 55^(\circ)=(VT)/(TU)`

Substituting the values, we have;

`sin \ 55^(\circ)=(82)/(TU)`

Simplifying, we have;

`TU=(82)/(sin \ 55^(\circ))`

`TU=(82)/(0.819)`

`TU=100.1`

Thus, the length of TU is 100.1 feet.