On the same side of tower, two objects are located. Observed from the top of the tower, their angles of depression are 45° and 60°. If the height of the tower is 150 m, the distance between the objects is.

A. 63.5 m B. 76.9 m C. 86.7 m D. 90 m Answer: Option A
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Solution(By Apex Team)

Height and Distance solution image Given that height of the tower is 150 m Let the two objects be placed at point C and D respectively In △ABC $\begin{array}{l} \tan 60^{\circ}=\frac{150}{\mathrm{BC}} \\ \Rightarrow \mathrm{BC}=\frac{150}{\sqrt{3}}\quad(\text { Take } \sqrt{3}=1.73) \end{array}$ and in △ABD $\tan 45^{\circ}=\frac{150}{\mathrm{BD}} \Rightarrow \mathrm{BD}=150 \mathrm{~m}$ Now, Distance between objects is; $\mathrm{CD}=\mathrm{BD}-\mathrm{BC}$ $\begin{array}{l} =\left(150-\frac{150}{\sqrt{3}}\right) \mathrm{m} \\ =\left[\frac{150(\sqrt{3}-1)}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}\right] \mathrm{m} \\ =50(3-\sqrt{3}) \mathrm{m} \\ =(50 \times 1.27) \mathrm{m} \\ =63.5 \mathrm{~m} \end{array}$