Question

use the figure below to find the exact value of the trigonometric function of angle a. sin(a) use the pythagorean theorem to find the hypotenuse of the right triangle. how is sin(a) defined resources ebook introduction to trigonometric functions using triangles finding trig functions using a right triangle learn by example determine six trig functions from a triangle example video

Explanation:

Step1: Find the hypotenuse

By the Pythagorean theorem $c^{2}=a^{2}+b^{2}$, where $a = 8$ and $b=20$. So $c=\sqrt{8^{2}+20^{2}}=\sqrt{64 + 400}=\sqrt{464}=4\sqrt{29}$.

Step2: Define sine function

The sine of an angle in a right - triangle is defined as $\sin(A)=\frac{\text{opposite}}{\text{hypotenuse}}$. The side opposite to angle $A$ is the side with length $20$, and the hypotenuse is $4\sqrt{29}$. So $\sin(A)=\frac{20}{4\sqrt{29}}=\frac{5}{\sqrt{29}}=\frac{5\sqrt{29}}{29}$.

Answer:

$\frac{5\sqrt{29}}{29}$