Presented by RAMA KRISHNA RAO AD KV, PICKET

HEIGHTS & DISTANCES

REVISION

QNo. From a point 100m above a lake , the angle of elevation of a stationary cloud is 300 and the angle of depression of reflection of the cloud in the lake is 600. Find the height of the cloud from the lake.

100m

300

600

h

A

BC

D

E

F

Sol:Let BC – surface of the lake

A – point of observation

AB = 100m

ED = h (height of the cloud)

---------(i)

In rt. ∆EDA

Hence, the height of the cloud from the surface of the lake = h + DC = 100 + 100 = 200m

100m

300

600

h

A

BC

D

E

F

In rt. ∆FDA

A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. Theangle of elevation of the balloon from the eyes of the girl at any instant is 60°. After some time, the angle ofelevation reduces to 30°.Find the distance travelled by theballoon during the interval.

Sol:

Que:

1.2

m

88.

2 m

600 300

E

B

C

D

A

F

1.2

m

88.2

m

600 300

E

B

C

D

A

F

Let AC = 88.2m (height of the balloon from the ground)BC = 1.2m (height of the girl.

AB = AC – BC = 88.2 – 1.2 = 87m

In rt ∆ ABD In rt ∆ EFD

BF = 100.34 mThe distance travelled by the balloon during the interval is 100.34m

PRACTICE QUESTIONS

A man on deck of ship is 10m above water level. He observes that the angle of elevation of top of a hill is 600 and angle of depression of base of hill is 300. Calculate the distance of hill from ship and height of the hill.

tantan

tantan

From an aeroplane vertically above a straight horizontal plane, the angles of depression of two consecutive kilometers stones on opposite sides of the aeroplane are found to be α and β. Show that height of the aeroplane is

.Que 1:

Que 2: