Question

Amit is standing on a horizontal plane finds a bird flying at a distance of 200 m from him at an elevation of 30° people standing on the roof of a 50 M high building find the angle of elevation of the same but to be 45° Amit and Deepak are on opposite sides of the bird find the distance of the bird from Deepak

Answer 1

Answer:

The distance of the bird from deepak is 70.7 meters.

Step-by-step explanation:

Let Amit is standing at point A, bird at point B, deepak at point D

height of the bird = BC, let E be a point on BC corresponding to point D at 50 m height

given,

AB = 200

∠A = 30°

∠D = 45°

In triangle ABC

Sin 30 = BC/AB

=> 1/2 = BC/200

=> BC = 100 m

=> BE = BC- EC = 100 - 50 = 50 m

In triangle,BED,

sin 45 = BE/BD

=> 1/√2 = 50/BD

=> BD = 50√2 = 70.7 m

Hence the distance of the bird from deepak is 70.7 meters.

Answer 2

Answer:

50√2 m

Step-by-step explanation:

Amit,standings on a horizontal plane,finds a bird flying at a distance of 200m from him at an elevation of 30°. Deepak standing on the roof of 50m high building,finds the angle of elevation of the same bird to be 45°.Amit and Deepak are on opposite sides of the bird . Find the distance of bird from Deepak

Amit form an right angle triangle with bird where base angle = 30° (Elevation Angle) and hypotenuse = 200m (Distance)

Let say height of bird from ground = h m

Sin 30° = h / 200   ( perpendicular / hypotenuse)

=> 1/2 = h/200     (Sin 30° = 1/2)

=> h = 100 m  

Deepak standing on height of 50 m

so bird height from deepak = 100 - 50 = 50 m

Angle of Elevation = 45°

Sin45° = 50/(distance of bird from Deepak)

=> 1/√2 = 50/(distance of bird from Deepak)

=> distance of bird from Deepak = 50√2 m