Properties of 45°-45°-90° triangles:
- Legs are congruent
- the hypotenuse is equal to √(2) times the legs' length
Properties of 30°-60°-90° triangles:
- If the short leg's length is x, then
- the hypotenuse is equal to 2x
- the long leg is equal to x√(3)
With these properties in mind, let's solve for our variables.
Triangle no. 1: 45°-45°-90°
Leg = d
Hypotenuse = 4
Given the properties, an as yet unknown number times √(2) is equal to 4. This unknown number is the legs' length, or d.
d√(2) = 4
d ≈ 2.82
Triangle no. 2: 30°-60°-90°
Short leg = 5
Long leg = h = 5√(3)
Hypotenuse = 5(2)
5√(3) ≈ 8.66
Answer:
d ≈ 2.82
h ≈ 8.66
