Answer:
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:
[tex]QSR+TSQ=180[/tex]
We already know that TSQ is 150, thus:
[tex]QSR+150=180[/tex]
Subtract:
[tex]QSR=30[/tex]
So, QSR is 30 degrees.
Find tangent of 30 degrees.
[tex]\tan(30)[/tex]
1) If you know the unit circle:
At 30 degrees, our coordinate is:
[tex](\frac{\sqrt3}{2},\frac{1}{2}})[/tex]
So, our answer would be:
[tex]\tan(30)=\frac{\frac{1}{2}}{\frac{\sqrt3}{2}}[/tex]
Simplify:
[tex]\tan(30)=\frac{1}{\sqrt{3}}=\frac{\sqrt{3}}{3}[/tex]
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:
[tex]\tan(30)=opp/adj[/tex]
Substitute x for opposite and x√3 for adjacent. Thus:
[tex]\tan(30)=\frac{x}{x\sqrt3}[/tex]
Remove the x:
[tex]\tan(30)=\frac{1}{\sqrt3}[/tex]
Multiply both layers by √3. So:
[tex]\tan(30)=\frac{1}{\sqrt3}=\frac{\sqrt3}{3}[/tex]
Our answer is A :)
