Question

Find tangent and explain the process

Answer 1

A

Explanation:

So we want to find the tangent of Angle QSR.

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

`QSR+TSQ=180`

We already know that TSQ is 150, thus:

`QSR+150=180`

Subtract:

`QSR=30`

So, QSR is 30 degrees.

Find tangent of 30 degrees.

`\tan(30)`

1) If you know the unit circle:

At 30 degrees, our coordinate is:

`((\sqrt3)/(2),(1)/(2)})`

So, our answer would be:

`\tan(30)=((1)/(2))/((\sqrt3)/(2))`

Simplify:

`\tan(30)=(1)/(√(3))=(√(3))/(3)`

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:

`\tan(30)=opp/adj`

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

`\tan(30)=(x)/(x\sqrt3)`

Remove the x:

`\tan(30)=(1)/(\sqrt3)`

Multiply both layers by √3. So:

`\tan(30)=(1)/(\sqrt3)=(\sqrt3)/(3)`

Our answer is A :)