Find tangent and explain the process

A

Step-by-step explanation:

So we want to find the tangent of Angle QSR.

First, note that Angle QSR and Angle TSQ forms a supplementary angle. Thus:

We already know that TSQ is 150, thus:

Subtract:

So, QSR is 30 degrees.

Find tangent of 30 degrees.

1) If you know the unit circle:

At 30 degrees, our coordinate is:

So, our answer would be:

Simplify:

2) If you don't know the unit circle.

Recall that 30-60-90 is a special right triangle.

The side opposite to 30 is x, the side adjacent to 30 is x√3, and the hypotenuse is 2x.

Therefore, tangent of 30 is opposite over adjacent. Thus:

Substitute x for opposite and x√3 for adjacent. Thus:

Remove the x:

Multiply both layers by √3. So:

Our answer is A :)