MP Board · Class 10 · Mathematics · Applications of TrigonometryThe angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, find the height of the building.
Let the height of the building be $h$ and the distance between the building and tower be $x$. From the tower's foot, $\tan 60^\circ = \frac{50}{x} \implies \sqrt{3} = \frac{50}{x} \implies x = \frac{50}{\sqrt{3}}$. From the building's foot, $\tan 30^\circ = \frac{h}{x} \implies \frac{1}{\sqrt{3}} = \frac{h}{x} \implies h = \frac{x}{\sqrt{3}}$. Substituting $x$, $h = \frac{50/\sqrt{3}}{\sqrt{3}} = \frac{50}{3}$ m.
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Applications of Trigonometry.
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Applications of Trigonometry.
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Applications of Trigonometry.