Question

score: 3/10 current time: 52.0 find: sin a
right triangle with right angle, vertical leg 63 (labeled b), horizontal leg 16 (labeled a), hypotenuse 65
the figure is not drawn to scale
answer
options:
\\(\frac{63}{65}\\), \\(\frac{16}{63}\\), \\(\frac{63}{16}\\), \\(\frac{16}{65}\\)

Explanation:

Step1: Recall sine definition

In a right triangle, $\sin\theta = \frac{\text{opposite}}{\text{hypotenuse}}$.

Step2: Identify sides for $\angle A$

For $\angle A$, opposite side is $63$, hypotenuse is $65$.

Step3: Calculate $\sin A$

$\sin A = \frac{63}{65}$.

Answer:

$\frac{63}{65}$ (corresponding to the first option: $\boldsymbol{\frac{63}{65}}$)