Question

1. find the approximate value of x:

a 90.23
b 95.84
c 76.05
d 88.54

Explanation:

Step1: Identify trigonometric ratio

In right triangle \(PQR\), \(\angle P = 53^\circ\), hypotenuse \(PR = 120\) m, and \(x = RQ\) (opposite to \(\angle P\)). Use \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\).
\(\sin(53^\circ)=\frac{x}{120}\)

Step2: Solve for \(x\)

Rearrange: \(x = 120\times\sin(53^\circ)\). \(\sin(53^\circ)\approx0.7986\).
\(x\approx120\times0.7986 = 95.832\approx95.84\)

Answer:

b. 95.84