Question

question
find the value of sin b rounded to the nearest hundredth, if necessary.

Explanation:

Step1: Find the hypotenuse

Use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(a = 16\) and \(b=30\). So \(c=\sqrt{16^{2}+30^{2}}=\sqrt{256 + 900}=\sqrt{1156}=34\).

Step2: Recall sine - definition

The sine of an angle in a right - triangle is defined as \(\sin B=\frac{\text{opposite}}{\text{hypotenuse}}\). For angle \(B\), the opposite side to \(B\) is \(DC = 16\) and the hypotenuse \(BD=34\).

Step3: Calculate \(\sin B\)

\(\sin B=\frac{16}{34}\approx0.47\)

Answer:

\(0.47\)