Question

Nisha is looking out the window of her apartment building at a sculpture in a park across the street. The top of Nisha's window is 60 feet from the ground. The angle of depression from the top of Nisha's window to the bottom of the sculpture is 25°. How far away from the building is the sculpture? Round your answer to the nearest hundredth. 25. 36 feet 27. 98 feet 100. 22 feet 128. 67 feet.

Answer 1

Angle of depression is the angle from horizontal line to the line of sight.  The distance from building of the sculpture is: Option d: 128. 67 feet.

What is angle of depression?

You look straight parallel to ground. But when you have to watch something down, then you take your sight up by moving your head down. The angle from horizontal to the point where you stopped your head is called angle of depression.

For the given case, referring to the figure, we have:

Length of BC = |BC| = 60 ft.

Length of AB = |AB| = x ft (distance of sculpture from building horizontally).

∠CAB = 25°

Thus, using tangent ratio from point of view of ∠CAB, we get:

$\tan(25^\circ) = \dfrac{|BC|}{|AB|} = \dfrac{60}{x}\\\\x = \dfrac{60}{tan(25^\circ)} \approx 128.67 \: \rm ft$

(value of tan25° was calculated from calculator available online)

Thus,

The distance from building of the sculpture is: Option d: 128. 67 feet.

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