A boy standing on a ground sees an angle of elevation of 30° to the top of a tower 50 m high . When

M4maths Previous Puzzles

20 Oct 2022 Geometry

A boy standing on a ground sees an angle of elevation of 30° to the top of a tower 50 m high . When he started walking towards tower in a straight line, after 3 minutes he observes an angle of elevation of a top of a tower as 60°, then walking speed of a boy is

OPtion

1) 2 km/hr
2) 4 km/hr
3) 1.3333 km/hr
4) 1.5147 km/hr
5) 2.8284 km/hr
6) 2.3094 km/hr
7) 1.1547 km/hr
8) 0.6666 km/hr
9) 1.7320 km/hr
10) None of these

Solution

Let distance walked by boy from starting point where he observes an angle of elevation 30° and the point where he observes angle of elevation 60° be 'x' m and the distance of base of a tower from starting point be 'y' m.
Then, trignometric ratios:
tan 30 = 50/y
1/√3=50/y ⇒ y=50√3 ---(i)
Also, tan 60 = 50/(y-x)
√3=50/(y-x) ⇒ y-x=50/√3 ---(ii)
Substituting value of y from (i) into (ii), we get x=100√3
Now, the distance travelled 'x' in 3 minutes is 100/√3 m, so distance/hr=(60/3)*100/√3=1154.7 m
Speed=1.1547 km/hr
Correct Option 7)

Correct Option: 7 Best Solution (0)