Question

find cosθ, where θ is the angle shown. give an exact value, not a decimal approximation. triangle with hypotenuse 8, opposite side 5, right angle, angle θ at the left vertex cosθ = blank

Explanation:

Step1: Recall cosine definition

In a right triangle, $\cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}}$. First, find the adjacent side length using Pythagoras: $a = \sqrt{8^2 - 5^2} = \sqrt{64 - 25} = \sqrt{39}$.

Step2: Apply cosine formula

Adjacent side to $\theta$ is $\sqrt{39}$, hypotenuse is 8. So $\cos\theta = \frac{\sqrt{39}}{8}$.

Answer:

$\frac{\sqrt{39}}{8}$