Question

use the following right triangle to find cos θ. note: enter the exact, fully simplified and rationalized answer. cos θ =

Explanation:

Step1: Recall cosine formula

In a right - triangle, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. First, find the hypotenuse using the Pythagorean theorem $c = \sqrt{a^{2}+b^{2}}$, where $a = 1$ and $b = 6$.

Step2: Calculate the hypotenuse

$c=\sqrt{1^{2}+6^{2}}=\sqrt{1 + 36}=\sqrt{37}$.

Step3: Find $\cos\theta$

Since the adjacent side to $\theta$ is $1$ and the hypotenuse is $\sqrt{37}$, then $\cos\theta=\frac{1}{\sqrt{37}}$. Rationalize the denominator: $\cos\theta=\frac{1\times\sqrt{37}}{\sqrt{37}\times\sqrt{37}}=\frac{\sqrt{37}}{37}$.

Answer:

$\frac{\sqrt{37}}{37}$