Question

Given right triangle GYK, what is the value of tan(G)?

A. 1/2
B. √3/2
C. 2√3/3
D. √3

Answer 1

Option D. √3

Explanation:

In a right angle triangle tan∅ = height / Base

Height means opposite side of the angle and base is the adjacent side of the given angle.

So tan (G) = height / Base

Now we can calculate the value of tan ∅ by two ways.

1) If the sides are given.

2) By using sin/cos/tan table for the given value of the angle.

Here ∠YGK is given as 60° and we have to find the value of tan 60° then by using sin/cos/tan table we get the value

tan (G) = tan 60° = √3.

Therefore option D. is the correct answer.

Answer 2

OPTION D (√3)

Explanation:

By definition, the tangent of a right triangle is:

`tan\alpha=opposite/adjacent`

Then, you have the right triangle GYK, you can find the tan(G) as you can see below:

Find KY as following:

`tan(30)=27/KY=\\KY=27/tan(30)\\KY=27√(3)`

Then, you have:

`tan(G)=27√(3)/27`

When you simplify, you obtain:

`tan(G)=√(3)`