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 ΔTUV is a right triangle. The measure of ∠V=90°, the measure of ∠U=55°, and VT = 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=82` and
`hyp =TU`

Substituting the values, we get;

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

Simplifying, we get;

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

`TU=(82)/(0.819)`

`TU=100.12`

Rounding off to the nearest tenth, we get;

`TU=100.1`

Thus, the length of TU is 100.1 feet.