Question

for the triangle above, find sin a. a. 0.724 b. 49° c. 50° d. 0.69 please select the best answer from the choices provided

Explanation:

Step1: Recall sine - definition

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. For $\angle A$, the opposite side to $\angle A$ is $BC = 20$ and we need to find the hypotenuse $AB$.

Step2: Use the Pythagorean theorem

By the Pythagorean theorem $AB=\sqrt{AC^{2}+BC^{2}}$. Given $AC = 21$ and $BC = 20$, then $AB=\sqrt{21^{2}+20^{2}}=\sqrt{441 + 400}=\sqrt{841}=29$.

Step3: Calculate $\sin A$

$\sin A=\frac{BC}{AB}=\frac{20}{29}\approx0.69$.

Answer:

D. 0.69