Question

find: cos a
right triangle with right angle, vertical leg labeled 33 (side b), horizontal leg labeled 56 (side a), hypotenuse labeled 65
the figure is not drawn to scale
answer
options: (\frac{33}{56}), (\frac{33}{65}), (\frac{56}{33}), (\frac{56}{65})

Explanation:

Step1: Recall cosine definition

In a right triangle, $\cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}}$ for an acute angle $\theta$.

Step2: Identify sides for $\angle A$

For $\angle A$, adjacent side is 56, hypotenuse is 65.

Step3: Calculate $\cos A$

$\cos A = \frac{\text{adjacent to } A}{\text{hypotenuse}} = \frac{56}{65}$

Answer:

$\frac{56}{65}$ (corresponding to the option with $\frac{56}{65}$)