Question

In ΔTUV, the measure of ∠V=90°, the measure of ∠T=16°, and VT = 4.9 feet. Find the length of TU to the nearest tenth of a foot.

Answer 1

Given:

Given that TUV is a right triangle.

The measure of ∠T is 16°

The length of VT is 4.9 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;

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

where $\theta=16^{\circ}$, adj = TV and hyp = TU

Thus, we get;

$cos \ 16^{\circ}=\frac{4.9}{TU}$

Simplifying, we get;

$TU=\frac{4.9}{cos \ 16^{\circ}}$

$TU=\frac{4.9}{0.9613}$

$TU=5.097$

Rounding off to the nearest tenth, we get;

$TU=5.1$

Thus, the length of TU is 5.1 feet.