Home
Class 10
MATHS
A man standing on the deck of a ship, wh...

A man standing on the deck of a ship, which is 10m above water level. He observes the angle of elevation of the top of a hill as `60^0` and the angle of depression of the base of the hill as `30^0dot` Calculate the distance of the hill from the ship and the height of the hill.

Text Solution

Verified by Experts

Let the height of the hill AB = h m and let the position of man at 10 m above the sea-level is D.
Let `BC=x m rArr DE=x m `
In right `DeltaDCB`,
tan30^(@)=(DC)/(BC) rArr 1/sqrt3=10/x rArr x=10sqrt3 m …(1)`
In right 60^(@)=(AE)/(DE) rArr sqrt3=(h-10)/x`
`:. xsqrt3=h-10 rArr10sqrt3xxsqrt3=h-10" [from(1)]"`
`rArr h=30+10=40m`
Hence, the distance of the hill from the ship id x i.e., `10sqrt3 m` and height of the hill is 40 m.
Promotional Banner

Topper's Solved these Questions

  • SOME APPLICATIONS OF TRIGONOMETRY

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise|32 Videos

  • SOME APPLICATIONS OF TRIGONOMETRY

    NAGEEN PRAKASHAN ENGLISH|Exercise Revision Exercise (short Answer Questions)|5 Videos

  • REAL NUMBERS

    NAGEEN PRAKASHAN ENGLISH|Exercise Revision Exercise Long Answer Questions|5 Videos

  • STATISTICS

    NAGEEN PRAKASHAN ENGLISH|Exercise Revision Exercise Long Answer Questions|4 Videos

Similar Questions

Explore conceptually related problems

A man standing on the deck of a ship, which is 8m above water level. He observes the angle of elevation of the top of a hill as 60o and the angle of depression of the base of the hill as 30o . Calculate the distance of the hill from the ship and the height of the hill.

A man standing on the deck of a ship, which is 10 m above water level, observes the angle of elevation of the top of a hill as 60^@ and the angle of depression the base of hill as 30^@ . Find the distance of the hill from the ship and the height of the hill.

A man on the deck of a ship is 10m above the water level. He observes that the angle of elevation of the top of a cliff is 45o and the angle of depression of the base is 30o . Calculate the distance of the cliff from the ship and the height of the cliff.

A man stands 9 m away from a flag-pole. He observes that angle of elevation of the top of the pole is 28^(@) and the angle of depression of the bottom of the pole is 13^(@) .Calculate the height of the pole .

The angle of elevation of the top of a hill at the foot of a tower is 60^@ and the angle of elevation of the top of the tower from the foot of the hill is 30^@ . If the tower is 50 m high, what is the height of the hill?

From the top of a 7 m high building, the angle of elevation of the top of a tower is 60° and the angle of depression of the foot of the tower is 30°. Find the height of the tower.

A vertical pole and a vertical tower are on the same level ground in such a way that from the top of the pole the angle of elevation of the top of the tower is 60^(@) and the angle of depression of the bottom of the tower is 30^(@) . Find : the height of the pole, if the height of the tower is 75 m

A vertical pole and a vertical tower are on the same level ground in such a way that from the top of the pole the angle of elevation of the top of the tower is 60^(@) and the angle of depression of the bottom of the tower is 30^(@) . Find : the height of the tower, it the height of the pole is 20 m ,

From the top of a 7m high building, the angle of elevation of the top of a cable tower is 60^(@) and the angle of depression of its foot is 45^(@) . Determine the height of the tower.

The angle of elevation of a cloud from a point 60m above a lake is 30^@ and the angle of depression of the reflection of cloud in the lake is 60^@ . Find the height of the cloud.