Question

in the diagram below, ( rt = 15 ) and ( mangle r = 63^{circ} ). find ( st ).
write your answer as a whole number or as a decimal rounded to the nearest tenth.
( st = )

Explanation:

Step1: Recall the sine function

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, in right - triangle \(RST\) with \(\theta = \angle R=63^{\circ}\), the side opposite to \(\angle R\) is \(ST\), and the hypotenuse is \(RT = 15\). So, \(\sin R=\frac{ST}{RT}\).

Step2: Substitute the known values

Since \(RT = 15\) and \(R = 63^{\circ}\), we have \(ST=RT\times\sin R\). Substituting the values, \(ST = 15\times\sin(63^{\circ})\).

Step3: Calculate the value

We know that \(\sin(63^{\circ})\approx0.891\). Then \(ST=15\times0.891 = 13.365\approx13.4\).

Answer:

\(13.4\)