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NTPC Graduate Tier 1 2025 Shift-2 📅 05 Jun, 2025

The angle of elevation of the top of a tower from a point on the ground, which is 48 m away from the foot of the tower is 30°. Find the height of the tower.

A
15√3 m
B
18√3 m
C
12√3 m
D
16√3 m
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NTPC Graduate Tier 1
2025 • 05 Jun, 2025 • Shift-2
The angle of elevation of the top of a tower from a point on the ground, which is 48 m away from the foot of the tower is 30°. Find the height of the tower.
Correct Answer
16√3 m
Trigonometric Modeling: Visualize a geometric right-angled triangle where the vertical perpendicular represents the unknown tower height (h), and the horizontal......
Ref/Book : NTPC Graduate Tier 1 2025
Ref. Subject Mathematics
Chapter -
Ref. Topic Heights and Distances
Pg. No -
💡 Analysis & Explanation
Trigonometric Modeling ▼
Visualize a geometric right-angled triangle where the vertical perpendicular represents the unknown tower height (h), and the horizontal base represents the ground distance (48 m).
Ratio Application ▼
The tangent function acts as the primary tool linking an angle to opposite and adjacent sides: tan(θ) = Perpendicular / Base.
Value Insertion ▼
Substitute the known data: tan(30°) = h / 48. The standard trigonometric value for tan(30°) is 1/√3.
Calculation Phase ▼
Thus, 1/√3 = h / 48. Cross-multiplying provides h = 48 / √3. To rationalize the denominator, multiply top and bottom by √3, yielding (48√3) / 3.
Conclusion ▼
Dividing 48 by 3 simplifies the final vertical height to exactly 16√3 m.
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