Question

63 65 c 8 16 63 —— 65 cos a a 30 34 8 16 c 1 —— 17 tan a

Explanation:

Step1: Verify first triangle (find $\cos A$)

First, identify right triangle $ABC$ with $\angle C=90^\circ$, $AC=63$, $AB=65$, $BC=16$.
For $\angle A$, adjacent side = $AC=63$, hypotenuse = $AB=65$.
$\cos A = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{63}{65}$

Step2: Solve second triangle (find $\tan A$)

Right triangle $ABC$ with $\angle B=90^\circ$, $AB=30$, $BC=16$, $AC=34$.
First, find the side opposite $\angle A$: $BC=16$.
Find the side adjacent to $\angle A$: $AB=30$.
$\tan A = \frac{\text{opposite}}{\text{adjacent}} = \frac{16}{30} = \frac{8}{15}$

Answer:

1. $\cos A = \frac{63}{65}$
2. $\tan A = \frac{8}{15}$