Question

use a calculator to find the length of each side. round to 4 decimal places.

( a = )
( b = )

Explanation:

Step1: Find the length of side \(a\)

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 8^{\circ}\) and the hypotenuse \(c = 15\). For side \(a\) (opposite to the angle \(8^{\circ}\)), we have \(\sin(8^{\circ})=\frac{a}{15}\). Then \(a = 15\times\sin(8^{\circ})\). Using a calculator, \(\sin(8^{\circ})\approx0.1392\), so \(a=15\times0.1392 = 2.0880\).

Step2: Find the length of side \(b\)

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\theta = 8^{\circ}\) and the hypotenuse \(c = 15\). For side \(b\) (adjacent to the angle \(8^{\circ}\)), we have \(\cos(8^{\circ})=\frac{b}{15}\). Then \(b = 15\times\cos(8^{\circ})\). Using a calculator, \(\cos(8^{\circ})\approx0.9903\), so \(b=15\times0.9903=14.8545\).

Answer:

\(a = 2.0880\)
\(b = 14.8545\)