Question

From a point p on a level ground, the angle of elevation of the top tower is 30. If the tower is 100 m high, the distance of point p from the foot of the tower is: 149 m 156 m 200 m 173 m

Answer 1

Please mark it as brainliest

Answer 2

Answer:  The correct option is (D) 173 m.

Step-by-step explanation:  Given that from a point P on a level ground, the angle of elevation of the top tower is 30 degrees and the tower is 100 m high.

We are to find the distance of the point P from the foot of the tower.

The picture is shown in the attached figure below. AB is the height of the tower and BP is the distance of the point P from the foot of the tower B.

The triangle ABP will be a right angled triangle, where

$m\angle ABP=90^\circ,~~m\angleAPB=30^\circ,~~AB=100~\textup{m},~~BP=?$

Using the trigonometric ratios, we have

$\tan m\angle ACB=\dfrac{perpendicular}{base}\\\\\\\Rightarrow \tan 30^\circ=\dfrac{AB}{BP}\\\\\\\Rightarrow \dfrac{1}{\sqrt3}=\dfrac{100}{BP}\\\\\Rightarrow BP=100\sqrt3\\\\\Rightarrow BP=173.20\\\\\Rightarrow BP=173~\textup{approx.}$

Thus, the distance of point P from the foot of the tower is approximately 173 meters.

Option (D) is CORRECT.