Question

In ΔBCD, the measure of ∠D=90°, the measure of ∠C=83°, and DB = 95 feet. Find the length of BC to the nearest tenth of a foot.

Answer 1

Answer:

95.7

Step-by-step explanation:

\sin C = \frac{\text{opposite}}{\text{hypotenuse}}=\frac{95}{x}

sinC=

hypotenuse

opposite

​

=

x

95

​

\sin 83=\frac{95}{x}

sin83=

x

95

​

x\sin 83=95

xsin83=95

Cross multiply.

\frac{x\sin 83}{\sin 83}=\frac{95}{\sin 83}

sin83

xsin83

​

=

sin83

95

​

Divide each side by sin 83.

x=\frac{95}{\sin 83}=95.7134\approx 95.7\text{ feet}

x=

sin83

95

​

=95.7134≈95.7 feet

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