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The angle of elevation of a tower from a point which is at a distance of 44 m from its foot is 60°. Find the height of the tower. (use 3=1.73)
76.12 m
48 m
68 m
56.37 m
76.12 m
Use the ratio of sides in a 30°-60°-90° triangle. The side opposite 60° is √3 times the side adjacent to 60°. Simply calculate 44 × 1.73.
Distance from foot of tower = 44 m, Angle of elevation = 60°, √3 = 1.73
tan(θ)=DistanceHeight
Use the ratio of sides in a 30°-60°-90° triangle. The side opposite 60° is √3 times the side adjacent to 60°. Simply calculate 44 × 1.73.
Students often use cos or sin instead of tan, or miscalculate the product of 44 and 1.73 by forgetting to account for the decimal correctly.
Identify Trigonometric Ratio
In a right-angled triangle, the tangent of the angle of elevation is the ratio of the height (opposite side) to the distance from the foot (adjacent side).
tan(60°)=44h
Substitute Known Values
We know that tan(60°)=3 and the problem provides 3=1.73.
1.73=44h
Calculate Height
Rearrange the equation to solve for h: h=44×1.73.
h=76.12 m
A is correct because the height of the tower is calculated as 44 multiplied by 1.73, which equals 76.12 m.
This concept is fundamental for Height and Distance problems in exams; always remember the standard tan values: tan(30°)=1/√3, tan(45°)=1, and tan(60°)=√3.
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