Question

the angle of elevation of the top of the hill from the top and the bottom of a building which is 50 metre high are 45 and 60 degree respectively find the height of a hill and the horizontal distance between the tower and the building

Answer 1

Welcome dear,

● Answer -

Height of the hill = 118.3 m

Distance between hill & building = 68.3 m.

◆ Explanation -

Let x be height of hill & y be the horizontal distance between hill & building.

From bottom of the building,

tan60° = x/y

y = x / tan60° ...(1)

From top of the building,

tan45° = (x-50)/y

y = (x-50) / tan45° ...(2)

Equating (1) & (2),

x / tan60° = (x-50) / tan45°

x.tan45° = (x-50).tan60°

x × 1 = (x-50) × 1.732

x = 1.732x - 50×1.732

1.732x - x = 86.6

x = 86.6 / 0.732

x = 118.3 m

Substitute this in (1),

y = x / tan60°

y = 118.3 / 1.732

y = 68.3 m

Therefore, height of the hill is 118.3 m & distance between hill & building is 68.3 m.

Thanks dear...

Answer 2

Step-by-step explanation:

Let AB be the hill and CD be the tower.

Angle of elevation of the hill at the foot of the tower is 60

o

, i.e., ∠ADB=60

o

and the angle of depression of the foot of hill from the top of the tower is 30

o

, i.e., ∠CBD=30

o

.

Now in right angled ΔCBD:

tan30 o = BD CD

BD=

tan30 oCD

BD= 3 1 50

BD=50 3 m

In right ΔABD:

tan60 o = BD AB

AB=BD×tan60

oAB=50 3 × 3

AB=50×3

AB=150 m

Hence, the height of the hill is 150 m.

solution