Question

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

answer attempt 1 out of 2
sin b =
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Explanation:

Step1: Identify triangle type and sides

Triangle \( BCD \) is right - angled at \( C \). So, for angle \( B \), the opposite side to \( B \) is \( DC = 16 \), the adjacent side is \( BC = 30 \), and the hypotenuse \( BD \) can be found using the Pythagorean theorem \( BD=\sqrt{DC^{2}+BC^{2}} \).
First, calculate \( BD \): \( BD=\sqrt{16^{2}+30^{2}}=\sqrt{256 + 900}=\sqrt{1156}=34 \).

Step2: Apply sine formula

The formula for the sine of an angle in a right - triangle is \( \sin\theta=\frac{\text{opposite}}{\text{hypotenuse}} \). For angle \( B \), the opposite side is \( DC = 16 \) and the hypotenuse is \( BD = 34 \).
So, \( \sin B=\frac{DC}{BD}=\frac{16}{34}\approx0.47 \) (rounded to the nearest hundredth).

Answer:

\( 0.47 \)