Q27 of 34 Page 1

From a point 100 m above a lake the angle of elevation of a stationary helicopter is 30° and the angle of depression of reflection of the helicopter in the lake is 60ᵒ. Find the height of the helicopter above the lake.


Let A be the point 100 m above lake and C be the helicopter and C' be the reflection of helicopter in water.


Given,


Angle of elevation of helicopter from point A, ∠CAQ = 30° [Let θ1]


Angle of depression of reflection from point A, ∠QAC' = 60° [Let θ2]


Also,


AB = PQ = 100 m …[1]


AQ = BP …[2]


CP = CP' [image distance is equal to object distance]


And let CQ = 'x'


∴CP = CQ + PQ = 100 + x


⇒ CP' = 100 + x …[3]


In ΔACQ



From [2]



⇒ BP = x√3 m …[4]


In ΔAQC'




[From [3]]


⇒ 3x = x + 200


⇒ 2x = 200


⇒ x = 100 m


And


Height of helicopter above lake = CP = x + 100


= 100 + 100 = 200 m


More from this chapter

All 34 →
25

Solve the following quadratic equation by applying the quadratic formula: p2x2 + (p2 – q2) x – q2 = 0

 26

The points A ( 1, -2 ), B ( 2, 3 ), C ( k, 2 ) and D ( - 4, - 3 ) are the vertices of a parallelogram. Find the value of k and the altitude of the parallelogram corresponding to the base AB.

 28

A donor agency ensures milk is supplied in containers, which are in the form of a frustum of a cone to be distributed to flood victims in a camp. The height of each frustum is 30 cm and the radii of whose lower and upper circular ends are 20 cm and 40 cm respectively. If this milk is available at the rate of Rs.35 per litre and 880 litres of milk is needed daily for a camp.

(a) Find how many milk containers are needed daily for the camp.


(b) What daily cost will it put on the donor agency?


(c) What value of the donor agency is depicted in this situation?

 29

The radii of two concentric circles are 13 cm and 8 cm. AB is a diameter of the bigger circle and BD is tangent to the smaller circle touching it at D and intersecting the larger circle at P, on producing. Find the length of AP.