Question

HELP!!!

What is the measure of an angle whose sine is √3/2 ?

a) 60

b) 45

c) 30

Answer 1

Trigonometry as taught is mostly about memorizing two lousy triangles, namely half a square and half an equilateral triangle. This one is half an equilateral triangle.

The respective opposite sides of the 30/60/90 triangle are in ratio
`1:√(3):2`

A sine of √3/2 is an opposite of √3 and a hypotenuse of 2, so opposite and hypotenuse of the 60 degree angle. (It's the mama bear, in the middle, just right.)

`\sin 60^\circ = (√(3))/(2)`

In the end you just have memorize the two tired triangles of trig.