Question

In ΔTUV, the measure of ∠V=90°, the measure of ∠U=43°, and VT = 88 feet. Find the length of UV to the nearest tenth of a foot.

Answer 1

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;

where , and

Substituting the values, we get;

Simplifying, we get;

Rounding off to the nearest tenth, we get;

Thus, the length of TU is 100.1 feet.

Explanation:

Answer 2

94.4

Explanation:

\tan U = \frac{\text{opposite}}{\text{adjacent}}=\frac{88}{x}

tanU=

adjacent

opposite

​

=

x

88

​

\tan 43=\frac{88}{x}

tan43=

x

88

​

x\tan 43=88

xtan43=88

Cross multiply.

\frac{x\tan 43}{\tan 43}=\frac{88}{\tan 43}

tan43

xtan43

​

=

tan43

88

​

Divide each side by tan 43.

x=\frac{88}{\tan 43}=94.3684\approx 94.4\text{ feet}

x=

tan43

88

​

=94.3684≈94.4 feet

Type into calculator and roundto the nearest tenth of a foot.