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
Answers
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...
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