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.

94.4

Step-by-step 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.