JEE Main · 2023 · 11 Apr 2023 · Shift 2 · Heights and Distances

The angle of elevation of the top P of a tower from the feet of one person standing due South of the tower is

4 5^{\circ}

and from the feet of another person standing due west of the tower is

3 0^{\circ}

. If the height of the tower is 5 meters, then the distance (in meters) between the two persons is equal to

Answer: (A)

Solution

Let the tower have height

h = 5

m. Let the person due South be at distance

d_{S}

and the person due West be at distance

d_{W}

from the base of the tower.

From the South:

tan 4 5^{\circ} = \frac{5}{d _{S}} \Rightarrow d_{S} = 5 m

From the West:

tan 3 0^{\circ} = \frac{5}{d _{W}} \Rightarrow d_{W} = 53 m

The two persons are at right angles to each other (one South, one West), so by Pythagorean theorem:

Distance = d_{S}^{2} + d_{W}^{2} = 25 + 75 = 100 = 10 m

JEE Main · 2023 · 11 Apr 2023 · Shift 2 · Single correct option