All Three Sides

Part of the Triangles section of Coddy's Geometry journey. Lesson 48 of 71.

When you know the short leg, each of the other two sides is one multiplication away. Multiply by √(3) to get the long leg. Multiply by 2 to get the hypotenuse. For a short leg of 4:

$A right triangle with angles 30 and 60 degrees, its short leg 4, its long leg y and its hypotenuse c$

Short leg 4: find the other two sides from it

y = 4√(3)

c = 2 × 4 = 8

The long leg is 4√(3), which is about 6.9, and the hypotenuse is 8. Always start from the short leg.

You can write the three facts as a system of three equations: x = 4, y = x √(3) and c = 2x. To solve it, substitute the known short leg into the other two equations. The sides of a 30-60-90 triangle are in the ratio 1 : √3 : 2. Remember it together with the 45-45-90 ratio 1 : 1 : √2. Between them, the two ratios cover every right triangle that has a 45°, a 30° or a 60° angle.