Question

From a tower 120 m high, the angle of depression of a car is ${60}^{\circ }$. What is the distance of the car from the foot of the tower?

• A. 40.28 m
• B. 59.28 m
• C. 69.28 m
• D. 79.28 m

Answer 1

The correct option is C 69.28 m

Let AB be the tower and C be the position of the car, such that $\angle DAC={60}^{\circ }$ where DA || BC.
Therefore, $\angle ACB={60}^{\circ }.$
In $\Delta ABC,$
$tan{60}^{\circ }=\frac{AB}{BC}$
$\Rightarrow \sqrt{3}=\frac{120}{BC}(As,AB=120m)$
$\Rightarrow BC=\frac{120}{\sqrt{3}}=40\sqrt{3}>>69.28m$
Hence, the correct answer is option (3).