Right Triangles

Ramps, ladders and ropes often sit at an angle. To work with a slanted length you split it into a part along the ground and a part straight up, and the tool for that is the right triangle.

The sides are named from the angle θ.

For the angle θ, the side next to it is the adjacent side, the side across from it is the opposite side, and the longest side is the hypotenuse:

sin θ = opposite / hypotenuse, cos θ = adjacent / hypotenuse

Example: a ramp is 8 m long and rises at 30°. Its height is the side opposite the angle: h = 8 sin 30° = 8 · 0.5 = 4 m.

The values you will use most: sin 30° = 0.5, cos 60° = 0.5 and sin 90° = 1.