Question

Given the diagram below, what is tan(60°)?
Triangle not drawn to scale

Answer 1

Option B.
`tan(60\°)=√(3)`

Explanation:

Let

y -----> the opposite side to angle of 60 degrees (or adjacent side to angle of 30 degrees)

x ----> the adjacent side to angle of 60 degrees (or opposite side to angle of 30 degrees)

we know that

The tangent of angle of 60 degrees is equal to divide the opposite side to angle of 60 degrees by the adjacent side to angle of 60 degrees

so

`tan(60\°)=(y)/(x)`

Find the value of y

Remember that

`cos(30\°)=(y)/(4)` ----> adjacent side to angle of 30 degrees by the hypotenuse

`cos(30\°)=(√(3))/(2)`

so

`(y)/(4)=(√(3))/(2)`

`y=2√(3)\ units`

Find the value of x

Remember that

`sin(30\°)=(x)/(4)` ----> opposite side to angle of 30 degrees by the hypotenuse

`sin(30\°)=(1)/(2)`

so

`(x)/(4)=(1)/(2)`

`x=2\ units`

Find the value of tan(60°)

`tan(60\°)=(y)/(x)`

substitute the values of x and y

`tan(60\°)=(2√(3))/(2)`

`tan(60\°)=√(3)`