Question

Given the diagram below, what is tan (60*)
OA. 4√2
OB. √3/2
OC. 4√3
OD. √3

Answer 1

D. √3

Explanation:

• This is a 30-60-90 triangle that has special rules concerning its side lengths.

• Let's call the length of the side opposite the 30° angle a.
• The length of the side opposite the 60° angle is a * √3.
• The length of the 90° (right) angle is 2a.

The tangent ratio is given by:

tan (θ) = opposite/adjacent, where

• θ is the reference angle.

• When the 60° angle is the reference angle, the side that is 8 * √3 units long is the opposite side.

• The side with an unknown length and opposite the 30° angle is the adjacent side.

• According to the 30-60-90 triangle rules, 8 is a and this is the length of the side opposite the 30° angle.

Thus, we plug in 8√3 for the opposite side and 8 for the adjacent side, which gives us:

tan (60) = (8√3) / 8

Thus reduces down to √3 so D. is the correct answer.