2023
Mathematics
JAMB
The angle of elevation and depression of the top and bottom of another building, measured from the top of a 24 m tall building, is 30° and 60°, respectively. Determine the second building's height.
A.
24 m
B.
32√3m
C.
24√3
D.
32 m
Correct Answer: 32 m
Explanation
The height of the second building H = h + 24 tan θ = opp/adj tan 30° = h/x ⟹3√3 = h/x ⟹x = √3 = 3h ⟹x = 3h/√3 ....(i) tan 60° = 24/x ⟹√3 = 24x ⟹x√3 = 24 ⟹x = 24/√3 ....(ii) Equate equation (i) and (ii) ⟹3h/√3 = 24/√3 ⟹ 3h = 24 ⟹h = 24/3 = 8m ∴The height of the second building = 8 + 24 = 32m
The height of the second building H = h + 24 tan θ = opp/adj tan 30° = h/x ⟹3√3 = h/x ⟹x = √3 = 3h ⟹x = 3h/√3 ....(i) tan 60° = 24/x ⟹√3 = 24x ⟹x√3 = 24 ⟹x = 24/√3 ....(ii) Equate equation (i) and (ii) ⟹3h/√3 = 24/√3 ⟹ 3h = 24 ⟹h = 24/3 = 8m ∴The height of the second building = 8 + 24 = 32mTHIS WEEK's
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