Exam

BITSAT

Year

2024

Subject

Mathematics

Chapter

Heights and Distances

BITSAT 2024 · Mathematics · Heights and Distances

From the top of a cliff 50 m high, the angles of depression of the...

From the top of a cliff 50 m high, the angles of depression of the top and bottom of a tower are observed to be $30^{{}^{\circ}}$ and $45^{{}^{\circ}}$. The height of tower is

Step-by-step solution

Accoding to condition, Let, height of tower =h In $\triangle A B D, \quad \tan 45^{{}^{\circ}}=\frac{A B}{B D} \Rightarrow B D=50 \mathrm{ m}$ Now, In $\triangle A C C^{\prime}$$\begin{aligned} & & \tan 30^{{}^{\circ}} & =\frac{A C^{\prime}}{C^{\prime} C} \\ \Rightarrow & & \frac{1}{\sqrt{3}} & =\frac{50-h}{50} \\ \Rightarrow & & 50 & =50 \sqrt{3}-h \sqrt{3} \\ \Rightarrow & & h \sqrt{3} & =50(\sqrt{3}-1) \\ & & h & =50\left(1-\frac{1}{\sqrt{3}}\right) \\ & & & =50\left(1-\frac{\sqrt{3}}{3}\right) \mathrm{m} \end{aligned}$$$