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 . (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.) a = 9, b = 12

Explanation:

Step1: Apply Pythagorean Theorem

In a right - triangle, $c^{2}=a^{2}+b^{2}$, where $c$ is the hypotenuse and $a$ and $b$ are the legs of the right - triangle. Here, $a = 9$ and $b = 12$. So, $c=\sqrt{a^{2}+b^{2}}=\sqrt{9^{2}+12^{2}}$.

Step2: Calculate the value of $c$

First, calculate $9^{2}=81$ and $12^{2}=144$. Then $a^{2}+b^{2}=81 + 144=225$. So, $c=\sqrt{225}=15$.

Answer:

15