Question

use the pythagorean theorem to find the length of the missing side of the right triangle. then find the value of each of the six trigonometric functions of θ. the length of the missing side of the right triangle is 15. (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.) find the sine of the angle θ. sin θ = (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Recall sine - function definition

The sine of an angle $\theta$ in a right - triangle is defined as $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$.

Step2: Identify opposite and hypotenuse

For angle $\theta$, the opposite side $a = 9$ and the hypotenuse $c=15$.

Step3: Calculate $\sin\theta$

$\sin\theta=\frac{a}{c}=\frac{9}{15}=\frac{3}{5}$

Answer:

$\frac{3}{5}$