## Using HTML5 Canvas to solve trigonometric problems

### 1.0 Description

From the origin of the circle, line \(h\)—the hypotenuse—stretches upwards at an angle \(\theta\) of \(30°\). The length 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 \(\text{cathetus A}\)—the adjacent—is on the X-axis until it reaches \(\text{cathetus B}\).

To find the adjacent cathetus, you need to do this formula: \(\cos(\theta) = \frac{\text{adjacent } (x)}{\text{hypotenuse } (h)}\)

- \(\theta\) 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: \(cos(30) = \frac{adjacent (x)}{hypotenuse (90)}\)

Then calculate \(sin(30)\):

`Math.cos(30*Math.PI / 180.0) = 0.86602540378443864676372317075294`

And you get: \(0.866 = \frac{x}{90}\)

Then use algebra and switch sides: \(\frac{x}{90} = 0.866\)

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 \(\text{cathetus B}\)—the opposite—on the Y-axis.

To find the opposite cathetus, you need to do this formula: \(\text{sin}(\theta)=\frac{\text{opposite}(y)}{\text{hypotenuse}(h)}\)

Just fill inn some blanks: \(sin(30) = \frac{opposite (y)}{hypotenuse (90)}\)

Then calculate \(sin(30)\):

`Math.sin(30*Math.PI / 180.0) = 0.5`

And you get: \(0.5 = \frac{y}{90}\)

Then use algebra and switch sides: \(\frac{y}{90} = 0.5\)

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!