Question

1. geometry *

for an angle with measure α in a right triangle, sin α = 5/13 and tan α = 5/12. what is the value of cos α?
a. 12/13
b. 12/√194
c. 12/√119
d. 13/12
o a
b
o c
o d

Explanation:

Step1: Recall tangent - sine - cosine relation

We know that $\tan\alpha=\frac{\sin\alpha}{\cos\alpha}$.

Step2: Rearrange the formula to solve for $\cos\alpha$

$\cos\alpha = \frac{\sin\alpha}{\tan\alpha}$.

Step3: Substitute given values

Given $\sin\alpha=\frac{5}{13}$ and $\tan\alpha=\frac{5}{12}$, then $\cos\alpha=\frac{\frac{5}{13}}{\frac{5}{12}}$.

Step4: Simplify the fraction

$\cos\alpha=\frac{5}{13}\times\frac{12}{5}=\frac{12}{13}$.

Answer:

A. $\frac{12}{13}$