Question

Find the exact value of tan θ.

A. √5
─
3

B. 3 √14
──
14

C. 3 √5
──
5

D. 2 √ 14

Answer 1

The answer is C.

Explanation:

Recall SohCahToa, where

`\displaystyle \tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}`.

In the triangle, the opposite (to angle θ) is
`6`, while the adjacent is
`2√(5)`.

By substitution:

`\displaystyle \tan(\theta)=(6)/(2\sqrt5)`

Simplify:

`\displaystyle (6)/(2√(5) ) \cdot(√(5) )/(√(5)) =(6√(5))/(2(5)) =(6√(5))/(10)=(3√(5) )/(5)`

The answer is C.