Question

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

Explanation:

Step1: Find the hypotenuse.

By the Pythagorean theorem $c=\sqrt{a^{2}+b^{2}}$, where $a = 1$ and $b=2$. So $c=\sqrt{1^{2}+2^{2}}=\sqrt{1 + 4}=\sqrt{5}$.

Step2: Recall the definition of secant.

The secant of an angle $\theta$ in a right - triangle is defined as $\sec\theta=\frac{\text{hypotenuse}}{\text{adjacent}}$. For angle $\theta$, the adjacent side to $\theta$ is $1$ and the hypotenuse is $\sqrt{5}$. So $\sec\theta=\frac{\sqrt{5}}{1}=\sqrt{5}$.

Answer:

$\sqrt{5}$