A pilot in an aeroplane observes that V...

A pilot in an aeroplane observes that Vashi bridge is one side of the plane and Worli sea - link is just on the oposite side . The angles of depressons of Vashi bridge and Wrli sea - link are `60^(@) and 30^(@)` respectively . If the aeroplane is at a height of ` 5500 sqrt(3m)` at that time , what is the distance between Vashi bridge and Wrli sea - link ?

Text Solution

Verified by Experts

The correct Answer is:

The distance between the Vashi bridge and Worli sea-link is 22 km.

Let P be the position of the plane . Q is a point on the ground such that the perpendicular distance ` QP = 5500sqrt(3) m`
V is the position of Vashi bridge and W the position of Worli sea- link
From the figure , ` angle PWQ = angle BPW = 30^(@)" "` ...(Alternate angles )
Now, in right angled ` Delta PVQ,`
` tan angle PVQ = tan 60^(@) = (PQ)/(VQ) :. sqrt(3) = (5500sqrt(3))/(VQ)`
` :. VQ = (5500sqrt(3))/(VQ) :. VQ = 5500 m " "` ... (1)
` :. VQ = (5500sqrt(3))/(VQ) " " :. VQ = 5500 m" "` ... (1)
In right angled `Delta PWQ` ,
` tan angle PWQ = tan 30^(@) = (PQ)/(WQ)`
` :. 1/(sqrt(3))= (5500sqrt(3))/(WQ)`
` :. WQ = 5500 sqrt(3) xx sqrt(3) :. WQ = 5500 xx3`
` :. WQ = 16500 m " "` ...(2)
` VW = VQ +QW " "...(V-Q-W)`
` = (5500+ 16500)m " "` ... [ From (1) and (2) ]
` :. VW = 22000 m = 22 km`

Topper's Solved these Questions

CHALLENGING QUESTIONS
NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise SECTION 3 (MODEL QUESTION PAPER FOR PRACTICE )|7 Videos
CHALLENGING QUESTIONS
NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise SECTION 3 (MODEL QUESTION PAPER FOR PRACTICE ) Choose the correct alternative :|3 Videos
CHALLENGING QUESTIONS
NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise EXAMPLE FOR PRACTICE|22 Videos
CIRCLE
NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise Challenging Questions|10 Videos

Similar Questions

Explore conceptually related problems

From a point an a bridge across river, the angles of depression of the banks on opposite sides of the river are 30^(@) and 45^(@) respectively. If the bridge is at a height of 3 m from the banks, find the width of the river.

The angles of elevation of an aeroplane from two places 10 km apart are found to be 60^(@) and 30^(@) respectively. Find the height of the aeroplane.

From a point on a bridge across a river, the angles of depression of the banks on opposite sides, of the river are 30° and 45° respectively. If the bridge is at a height of 3 m from the banks, find the width of the river.

From a point A on a bridge across a river, the angles of deression of the banks on opposite side of the river are 30^@ and 45^@ , respectively. If the bridge is at a height of 9 m from the suface of river, then find the width of the river.

From a point of a bridge across a riuver, the angles of depression of the banks on opposite sides of the river are 30^(@) and 45^(@) , respectively. IF the bridge is at a height of 10 m from the banks, then find the width of the river. (Use sqrt3=1.73 )

From a point on a bridge across a river the angles of depression of the banks on opposite side of the river are 30o and 45o respectively. If bridge is at the height of 30m from the banks,find the width of the river.

Two men are on the opposite sides of a tower. They measure the angles of elevation of the top of the tower as 45^(@) and 30^(@) respectively. If the height of the tower is 40 m, then the distance between the men is

An aeroplane at an altitude of 1200 metres finds that two ships are sailing towards it in the same direction.The angles of depression of the ships as observed from the aeroplane are 60o and 30o respectively.Find the distance between the two ships.

Two ships are sailing in the sea on the tow sides of a light house . The angles of elevation of the top of the light house as observed from the two ships are 30^(@)and45^(@) respectively . If the light house is 100 m high , the distance be - tween the two ships is :(take sqrt(3)=1.73)

Two ships are sailing in the sea on the either side of the lighthouse.The angles of depression of two ships as observed from the top of the lighthouse are 60^(@) and 45^(@) ,respectively.If the distance between the ships is 100((sqrt(3)+1)/(sqrt(3)))m, then find the height of the lighthouse

NAVNEET PUBLICATION - MAHARASHTRA BOARD-CHALLENGING QUESTIONS-SECTION 3 (MODEL QUESTION PAPER FOR PRACTICE ) Solve any one of the following subquestions :

A pilot in an aeroplane observes that Vashi bridge is one side of the...
Text Solution
|
Solve any one of the following subquestions : Draw a circle with c...
Text Solution
|