### Trigonometry Problems

#### 1.0 Description

From the origin of the circle, line h — the hypotenuse — stretches upwards at an angle θ of 30°. The lenght of the line is equal to the radius of the circle (in this case 90px).

#### 1.1. Finding The Adjacent

Based on the previous information we will find how long cathetus A — the adjacent — is on the X-axis until it reaches cathetus B.

To find the adjacent cathetus, you need to do this formula: cos(θ) = adjacent (x) / hypotenuse (h)
θ stands for the angle
x stands for the unknown length of the adjacent cathetus
...and h stands for the hypotenuse.
Just fill inn some blanks: cos(30) = adjacent (x) / hypotenuse (90)
Then calculate sin(30): `Math.cos(30*Math.PI / 180.0) = 0.86602540378443864676372317075294`
And you get: 0.866 = x / 90
Then use algebra and switch sides: x / 90 = 0.866
Use algebra again and move a number away from the unknown so it is possible to calculate, however according to the rules of algebra it means the division operator must also change to a multiplication operator (the opposite operator), so we get: x = 0.866 * 90
Then calculate, and you find that x = 77.942286340599478208735085367764

#### 1.2 Finding The Opposite

Based on the previous information we will find the height of cathetus B — the opposite — on the Y-axis.

To find the opposite cathetus, you need to do this formula: sin(θ) = opposite (y) / hypotenuse (h)
Just fill inn some blanks: sin(30) = opposite (y) / hypotenuse (90)
Then calculate sin(30): `Math.sin(30*Math.PI / 180.0) = 0.5`
And you get: 0.5 = y / 90
Then use algebra and switch sides: y / 90 = 0.5
Use algebra again and move a number away from the unknown so it is possible to calculate, however according to the rules of algebra it means the division operator must also change to a multiplication operator (the opposite operator), so we get: y = 0.5 * 90
Then calculate, and you find that y = 45

And there you have it!