Question

question 15 of 25 what is the approximate value of sin b? a. 2.29 b. 0.92 c. 0.40 d. 1.09

Explanation:

Step1: Recall sine - definition

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. For $\angle B$, the side opposite to $\angle B$ is $AC = 16$ and the hypotenuse is $BC=17.46$.

Step2: Calculate $\sin B$

$\sin B=\frac{AC}{BC}=\frac{16}{17.46}\approx0.92$. However, we made a mistake above. For $\angle B$, the side opposite to $\angle B$ is $AC$, but we should use the side adjacent to $\angle B$ (which is $AB = 7$) and the hypotenuse $BC = 17.46$. So $\sin B=\frac{AB}{BC}=\frac{7}{17.46}\approx0.40$.

Answer:

C. 0.40