NECO 2002 Mathematics · Question 25

The angle of elevation of the top (T) of a palm tree from a point (R) on the ground is 30°. The distance from…

Question

The angle of elevation of the top (T) of a palm tree from a point (R) on the ground is 30°. The distance from R to the base (B) of the palm tree is 120m. What is the distance between T and R?

A.60m
B.60 $\sqrt{3}$ m
C.80 $\sqrt{3}$ m
D.120 $\sqrt{3}$ m
E.240m

Answer: C. 80 $\sqrt{3}$ m

Explanation written with AI and checked against the answer key

Analyze the question: The palm tree stands vertically, so triangle TBR has a right angle at B. The angle at R (the angle of elevation) is 30°. The side RB = 120 m is adjacent to this angle, and TR is the hypotenuse, which is what we need to find. Concept: In a right-angled triangle, cos θ = adjacent / hypotenuse. Solution: cos 30° = RB / TR √3/2 = 120 / TR TR = 120 × 2 / √3 = 240/√3 Rationalise the denominator: TR = (240 × √3) / (√3 × √3) = 240√3 / 3 = 80√3 m Answer: TR = 80√3 m (about 138. Check: The hypotenuse must be longer than 120 m. 80√3 ≈ 138.6 m, so it makes sense. Option A is shorter than the base, so it can't be right. Option E (240 m) would be the answer if the angle were 60°, since cos 60° = 1/2. Tip: Remember SOH-CAH-TOA. Label the sides first: here you know the adjacent side and want the hypotenuse, so use CAH (cosine). Also remember the exact values: cos 30° = √3/2, sin 30° = 1/2, tan 30° = 1/√3. In exams, always rationalise your final answer so it matches the options.

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The angle of elevation of the top (T) of a palm tree from a point (R) on the ground is 30°. The distance from…

Question

Answer: C. 803\sqrt{3}3​m

Answer: C. 80 $\sqrt{3}$ m