Use the Pythagorean Theorem to find the length of the sides "d" and "f." Explain your answer.

f = 10·√3/3 ≈ 5.774

d = 5·√3/3 ≈ 2.887

Step-by-step explanation:

The given parameters are;

The angles opposite the 90°, right angle, = 60° and 30°

The length of the leg opposite the 60° angle = 5

Therefore, by Pythagorean Theorem, we have;

f² = d² + 5²

However, by trigonometry, we have;

sin(θ) = Opposite/Hypotenuse

For the angle of the triangle, θ = 30°, we have;

sin(30°) = d/f = 0.5

∴ d = f × 0.5 = 0.5·f

Substituting the value of d in the equation given by Pythagorean Theorem, we have;

f² = (0.5·f)² + 5² = 0.25·f² + 5²

f² = 0.25·f² + 5²

f² - 0.25·f² = 5²

0.75·f² = 5²

f² = 5²/0.75 = 100/3

f = 10/√3 = 10·√3/3

f = 10·√3/3

d = f × 0.5 = 10·√3/3 × 0.5 = 5·√3/3

d = 5·√3/3.

12cm

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