Question

7
25
cos a
48
50
15
15/48
cos a
29
21
20
20/21
sin a
63
65
16

Explanation:

Step1: Recall cosine definition

For right triangle, $\cos A = \frac{\text{adjacent to } A}{\text{hypotenuse}}$

Step2: Solve first $\cos A$

In $\triangle ABC$ (right at B):
Adjacent to $A$: $AB=15$, Hypotenuse: $AC=50$
$\cos A = \frac{15}{50} = \frac{3}{10}$

Step3: Solve second $\cos A$

In $\triangle ABC$ (right at C):
Adjacent to $A$: $AC=20$, Hypotenuse: $AB=29$
$\cos A = \frac{20}{29}$

Step4: Recall sine definition

For right triangle, $\sin A = \frac{\text{opposite to } A}{\text{hypotenuse}}$

Step5: Solve $\sin A$

In $\triangle ABC$ (right at C):
Opposite to $A$: $BC=16$, Hypotenuse: $AB=65$
$\sin A = \frac{16}{65}$

Answer:

1. For the first triangle: $\boldsymbol{\cos A = \frac{3}{10}}$ (the given $\frac{7}{25}$ is incorrect)
2. For the second triangle: $\boldsymbol{\cos A = \frac{20}{29}}$ (the given $\frac{15}{48}$ is incorrect)
3. For the third triangle: $\boldsymbol{\sin A = \frac{16}{65}}$ (the given $\frac{20}{21}$ is incorrect)