From the base of a pole of height 20 meter, the angle of elevation of the top of a tower is 60°. The pole subtends an angle 30° at the top of the tower. Then the height of the tower is :
\(15\sqrt3\)
\(20\sqrt3\)
\(20+ 10\sqrt3\)
- 30
The Correct Option is D
Solution and Explanation
The correct answer is (D) : 30
tan 60° \(= \frac{h}{d} \)
tan 30° = \(\frac{20-h}{d}\)
\(⇒ \frac{20-h}{h/\sqrt{3}} = \frac{1}{\sqrt3}\)
\(⇒ \frac{2h}{3} = 20\)
⇒ h = 30 m
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Concepts Used:
Trigonometry
Trigonometry is a branch of mathematics focused on the relationships between angles and side lengths of triangles. It explores trigonometric functions, ratios, and identities, essential for solving problems involving triangles. Common functions include sine, cosine, and tangent.
Sine represents the ratio of the opposite side to the hypotenuse, cosine the adjacent side to the hypotenuse, and tangent the opposite side to the adjacent side. Trigonometry finds applications in various fields, including physics, engineering, and navigation. Understanding angles, circular functions, and the trigonometric table is fundamental in mastering this mathematical discipline