Question

consider this right triangle. enter the length of \\( \overline{rq} \\), to the nearest tenth.

Explanation:

Step1: Use sine function

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 55^{\circ}\), the hypotenuse \(RP = 9\), and the side opposite to \(\angle P\) is \(RQ\). So, \(\sin(55^{\circ})=\frac{RQ}{9}\).

Step2: Solve for \(RQ\)

Multiply both sides of the equation \(\sin(55^{\circ})=\frac{RQ}{9}\) by \(9\). We get \(RQ = 9\times\sin(55^{\circ})\). Using a calculator, \(\sin(55^{\circ})\approx0.8192\). Then \(RQ=9\times0.8192 = 7.3728\approx7.4\).

Answer:

\(7.4\)