Question

Identify the values of the variables. Give your answers in simplest radical form. PLEASE HELP!!

Answer 1

First question:

By definition of sine and cosine, we have

`\sin30^\circ=\frac h{\sqrt5}\implies h=\frac{\sqrt5}2`

`\cos30^\circ=\frac g{\sqrt5}\implies g=\frac{√(15)}2`

Second question:

By definition of tangent, we have

`\tan60^\circ=\frac{5\sqrt2}x\implies x=(5\sqrt2)/(\sqrt3)=\frac{5\sqrt6}3`

Then by Pythagoras' theorem,

`(5\sqrt2)^2+x^2=y^2\implies y=\sqrt{(5\sqrt2)^2+\left(\frac{5\sqrt6}3\right)^2}=\sqrt{50+\frac{50}3}=\sqrt{\frac{200}3}=\frac{10\sqrt6}3`