A girl on top of a storey building 36m high dropped a N10.00 note on the ground below. If the angle of…

Analyze the question: The girl is at the top of a building 36 m high. The note is on the ground. The angle of depression from her to the note is 35°. "How far is the money from the girl" means the straight-line distance, which is the line of sight (the hypotenuse).

Concept: The angle of depression from the top equals the angle of elevation from the ground (alternate angles). In the right-angled triangle:

• Opposite side to 35° = height of building = 36 m
• Hypotenuse = distance from the girl to the note

sin 35° = opposite / hypotenuse

Solution:

sin 35° = 36 / d

d = 36 / sin 35°

sin 35° ≈ 0.5736

d = 36 / 0.5736 ≈ 62.76 m

Check against the options: This matches option E (62.76 m). (Note that the horizontal distance would be 36 / tan 35° ≈ 51.4 m, which is not an option, so the question clearly wants the line-of-sight distance.)

Answer: E (62.76 m)

Tip: When a question asks for the distance "from the person" to an object, it usually means the slanted line of sight, so use sine or cosine with the hypotenuse. Remember SOH-CAH-TOA: since you have the opposite side and want the hypotenuse, use SOH (sine).