Two men are on opposite side of tower. They measure the angles of elevation of the top of the tower as 30° and 45° respectively. If the height of the tower is 50 meters, find the distance between the two men.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 136.6 m
Let the height of the tower = 50 m.
Two men are on opposite sides of the tower.
Distance of first man (angle = 30°)
$\tan 30^\circ = \frac{50}{x} \Rightarrow x = \frac{50}{\tan 30^\circ} = 50\sqrt{3} \approx 86.6 \text{ m}$
Distance of second man (angle = 45°)
$\tan 45^\circ = \frac{50}{y} \Rightarrow y = 50 \text{ m}$
Distance between the two men
Since they are on opposite sides:
$\text{Total distance} = x + y = 86.6 + 50 = 136.6 \text{ m}$