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Question

Difficulty: EasyAngles of Elevation, Depression, and Bearings

A vertical flagpole of height 15 m15\text{ m} standing on level ground casts a shadow of length 153 m15\sqrt{3}\text{ m}. Calculate the angle of elevation of the sun in degrees.

Answer: 30 degrees

Answer

The angle of elevation of the sun is 30 degrees.
The tangent of the angle of elevation is given by the height divided by the shadow length, tan⁡θ=15153=13\tan\theta = \frac{15}{15\sqrt{3}} = \frac{1}{\sqrt{3}}, which corresponds to an angle of 30∘30^\circ.

Step-by-Step Solution

1
Formulate the trigonometric relationship using the right triangle formed by the flagpole, the shadow, and the sunlight ray.
\tan\theta = \frac{\text{height of flagpole}}{\text{length of shadow}} = \frac{15}{15\sqrt{3}}
The tangent of an angle in a right-angled triangle is defined as the ratio of the opposite side to the adjacent side.
2
Simplify the ratio and evaluate the angle.
\tan\theta = \frac{1}{\sqrt{3}} \implies \theta = 30^\circ
The standard acute angle whose tangent value is 13\frac{1}{\sqrt{3}} is 30∘30^\circ.

Key Concept

Angle of Elevation and Trigonometric Ratios
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Topics

Angles of Elevation, Depression, and Bearings

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