a boy looks through a window of a building and sees a mango fruit on the ground 50m away from the foot of the…

Analyze the question: The window is 9 m above the ground and the mango is 50 m from the foot of the building. We need the angle of depression from the window down to the mango.

Concept: The angle of depression from the window equals the angle of elevation from the mango to the window (alternate angles). This gives a right-angled triangle:

• Opposite side = height of window = 9 m
• Adjacent side = horizontal distance = 50 m

So we use:

tan θ = opposite / adjacent

Solution:

tan θ = 9/50 = 0.18

θ = tan⁻¹(0.18)

Using tan 10° ≈ 0.1763 and tan 11° ≈ 0.1944:

• 0.18 is closer to 0.1763 than to 0.1944.
• More precisely, θ ≈ 10.2°.

So, to the nearest degree, θ = 10°.

Tip: Angle of depression is measured downward from the horizontal at the observer's eye, and it equals the angle of elevation from the object looking back up. For small angles, tan θ ≈ θ in radians, so 0.18 rad ≈ 10.3°, a quick check that the answer is near 10°.