Question

question 3 of 10
find cos θ.
right triangle with legs 16 and 12, hypotenuse 20, θ at the vertex with leg 12
a. 12/16
b. 16/13
c. 12/20
d. 16/20

Explanation:

Step1: Recall cosine definition

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

Step2: Identify sides for $\theta$

Adjacent to $\theta$ is 12, hypotenuse is 20.

Step3: Calculate $\cos\theta$

$\cos\theta = \frac{12}{20} = \frac{3}{5}$ (simplified, but option C is $\frac{12}{20}$ or $\frac{3}{5}$ equivalent). Wait, option C is $\frac{12}{20}$? Wait, let's check options again. Wait, the options: A is 12/16, B is 16/13 (invalid, hypotenuse is 20), C is 12/20, D is 16/20. Wait, adjacent to $\theta$: the angle $\theta$ is at the bottom right, so adjacent is the leg next to it (12), hypotenuse is 20. So $\cos\theta = \frac{12}{20}$, which is option C? Wait, no, wait: wait the triangle has legs 12 and 16, hypotenuse 20 (since $12^2 + 16^2 = 144 + 256 = 400 = 20^2$). So for angle $\theta$ (at the bottom right), the adjacent side is 12 (the horizontal leg), opposite is 16 (vertical leg), hypotenuse 20. So $\cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{12}{20}$, which is option C? Wait, but let's check the options again. Wait the user's image: options are A. 12/16, B. 16/13 (maybe typo, 13? No, hypotenuse is 20), C. 12/20, D. 16/20. So correct is C. Wait, but let's re-express:

Wait, step1: right triangle, cosine is adjacent over hypotenuse.

Step2: adjacent to $\theta$: the side next to $\theta$ that's not the hypotenuse. So $\theta$ is at the vertex with the right angle's adjacent (horizontal side) is 12, hypotenuse is 20.

Step3: so $\cos\theta = \frac{12}{20}$, which is option C.

Answer:

C. $\frac{12}{20}$