Question

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

Explanation:

Step1: Find hypotenuse with Pythagorean theorem

Let the two legs of the right - triangle be $a = 9$ and $b = 19$. By the Pythagorean theorem $c^{2}=a^{2}+b^{2}$, where $c$ is the hypotenuse. So $c=\sqrt{9^{2}+19^{2}}=\sqrt{81 + 361}=\sqrt{442}$.

Step2: Recall cosine definition

The cosine of an angle $A$ in a right - triangle is defined as $\cos(A)=\frac{\text{adjacent}}{\text{hypotenuse}}$. The side adjacent to angle $A$ is $9$ and the hypotenuse is $\sqrt{442}$. So $\cos(A)=\frac{9}{\sqrt{442}}$. Rationalizing the denominator, we get $\cos(A)=\frac{9\sqrt{442}}{442}$.

Answer:

$\frac{9\sqrt{442}}{442}$