Question

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Answer 1

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

1. the hypotenuse is equal to 2x
2. 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