Question

In ΔQRS, the measure of ∠S=90°, the measure of ∠Q=77°, and QR = 95 feet. Find the length of RS to the nearest tenth of a foot.

Answer 1

92.6

Step-by-step explanation:\text{SOH-CAH-TOA}

SOH-CAH-TOA

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

sinQ=

hypotenuse

opposite

​

=

95

x

​

\sin 77=\frac{x}{95}

sin77=

95

x

​

95\sin 77=x

95sin77=x

Cross multiply.

x=92.5652\approx \mathbf{92.6}\text{ feet}

x=92.5652≈92.6 feet

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

Q

R

S

92.6

95

(adjacent to ∠Q)

(opp. of ∠Q)

(hypotenuse)

77°