Question

Find the value of x and the value of y.

Answer 1

We have a right triangle with a 60 degree angle so this is 30/60/90, half an equilateral triangle, one of the two tired triangles of trig. I could solve it for the thousandth time or just tell you the truth: you need to memorize this one and the other one, 45/45/90, half a square. It's two lousy triangles; you'll be done in ten minutes. But it's ten minutes well spent.

The sides of 30/60/90 are in ratio $1:\sqrt{3}:2$ and here $y:x:10\sqrt{3}$ so

$\dfrac{y}{1} = \dfrac{x}{\sqrt{3}} = \dfrac{10\sqrt{3}}{2}$

$x = \sqrt{3} \cdot \dfrac{10\sqrt{3}}{2} = 15$

$y = 5\sqrt{3}$

Answer: x=15, y=5√3

Answer 2

The value of :-

x = 10root(3) sin 60°
= 10 (3)/2
= 15

y = 10root(3) cos60°
= 5root(3)