Trigonometry Problems
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 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!