1 Answer

Haduki · Answer 1 · 2019-11-11T12:55:58+0000

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,

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

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