Question

Analyze the diagram below and complete the instructions that follow.

Answer 1

Given:

ABC is a right triangle.

Opposite of C = AB = 6

Adjacent of C = BC = 8

Hypotenuse = AC = 10

To find:

The value of sin C.

Solution:

Using basic trigonometric ratio formula:

$\sin \theta = \frac{\text{Opposite of }\theta}{\text{Hypotenuse}}$

$\sin C = \frac{\text{Opposite of C}}{\text{Hypotenuse}}$

$\sin C = \frac{AB}{AC}$

$\sin C = \frac{6}{10}$

Cancel the common factors.

$\sin C = \frac{3}{5}$

The value of sin C is $\frac{3}{5}$.