Using tan(30°) = height/distance, we have distance = height/tan(30°) = 50/√3 = 25√3 m.

Distance = height / tan(angle) = 60 / 1 = 60 meters.

Distance = height / tan(angle) = 80 / √3 = 40 m.

Using tan(30°) = height/distance, we have 1/√3 = 10√3/distance. Therefore, distance = 10√3 * √3 = 30 m.

Using tan(30°) = height/distance, we have 1/√3 = 10√3/distance. Therefore, distance = 10√3 * √3 = 30 m.

Using tan(30°) = height/distance, we have distance = height/tan(30°) = 50/(1/√3) = 50√3 m.

Using tan(30°) = height/20, we have 1/√3 = height/20. Therefore, height = 20/√3 ≈ 11.55 m.

Using tan(45°) = height/shadow, we have 1 = height/20. Therefore, height = 20 m.

Height = shadow * tan(angle) = 20 * tan(30°) = 20 * (1/√3) = 20√3 meters.

Distance = height / tan(angle) = 15 / tan(30°) = 15√3 meters.

The solutions are x = π/4 and x = 3π/4.

The solutions are x = 0, π/2, π, 3π/2.

The solutions are x = nπ/2, where n is any integer.

Factoring gives sin(x)(sin(x) - 1) = 0, so x = 0, π/2, π, 3π/2.

The general solution is x = (2n+1)π/4, where n is any integer.

Factoring gives sin(x)(1 + 2cos(x)) = 0, leading to x = nπ or cos(x) = -1/2.

The general solution is x = (2n+1)π/3, where n is an integer.

The general solution is x = (2n+1)π/3, where n is an integer.

The general solutions are x = 7π/6 + 2nπ and x = 11π/6 + 2nπ.

Using the identity sin(a) = sin(b) gives x = nπ or x = (2n+1)π/3.

The general solution is x = nπ + (-1)^n π/4, where n is any integer.

Solving gives sin(x) = -√3/2, so x = 7π/6 and 11π/6.

The solutions are x = π/6 and x = 5π/6.

The solutions are x = π/6 and x = 5π/6.

Solving gives cos^2(x) = 1/3, so x = π/3, 2π/3, and their equivalents.

The solution is x = π/6 + 2nπ.

Factoring gives (sin(x) - 2)(sin(x) + 1) = 0, so sin(x) = 2 (not possible) or sin(x) = -1, giving x = 3π/2.

Factoring gives sin(x)(sin(x) - 1) = 0, so x = 0 and x = π.

Rearranging gives sin(x) = 1/3, which has solutions in the specified interval.

The solution is x = π/2.