Given right triangle gyk, what is the value of tan(g)?

a. 1/2
b. √3/2
c. 2√3/3
d. √3

OPTION D (√3)

Step-by-step explanation:

By definition, the tangent of a right triangle is:

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

Find KY as following:

Then, you have:

When you simplify, you obtain:

Option D. √3

Step-by-step 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.

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