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.
