Question

score: 1/10 current time: 20.9 find: cos a
right triangle with right angle, vertical leg 75 (labeled b), horizontal leg 40 (labeled a), hypotenuse 85
the figure is not drawn to scale
answer
options:
\\(\frac{75}{40}\\), \\(\frac{75}{85}\\), \\(\frac{40}{75}\\), \\(\frac{40}{85}\\)

Explanation:

Step1: Recall cosine definition

In a right triangle, $\cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}}$. For $\angle A$, adjacent side is 40, hypotenuse is 85.

Step2: Calculate $\cos A$

$\cos A = \frac{40}{85}$

Answer:

$\frac{40}{85}$ (corresponding to the option with $\frac{40}{85}$)