Question

question 15 of 30
cos \theta=\frac{9}{15}. find tan \theta.
a. \frac{9}{12}
b. \frac{12}{9}
c. \frac{15}{12}
d. \frac{12}{15}

Explanation:

Step1: Recall cosine definition

$\cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{9}{15}$, so adjacent = 9, hypotenuse = 15.

Step2: Calculate opposite side

Use Pythagorean theorem: $\text{opposite} = \sqrt{15^2 - 9^2} = \sqrt{225 - 81} = \sqrt{144} = 12$.

Step3: Recall tangent definition

$\tan\theta = \frac{\text{opposite}}{\text{adjacent}} = \frac{12}{9}$.

Answer:

B. $\frac{12}{9}$