Two buildings are facing each other on a road of width 12 metre. From the top of the first building, which is 10 metre high, the angle of elevation of the top of the second is found to be 60°. What is the height of the second building?

Let AB represent height of first building and CD represent height of second building.BD is the width of the road.Draw AMCDGiven Angle of elevation CAM = 60˚Given AB = 10BD = 12In AMDB , D = B = 90˚Since AMCD , M = 90˚A = 90˚ [Angle sum property of quadrilateral]Since each angle equal to […]

From the top of a lighthouse, an observer looking at a ship makes angle of depression of 60°. If the height of the lighthouse is 90 metre, then find how far the ship is from the lighthouse. (√3 =1.73)

Let C represent position of ship and AB represent height of the light houseGiven AB = 90mAngle of depression DAC = 60˚Here BCAD.BCA = DAC [Alternate interior angles]BCA = 60˚In ABC tan60 = AB/BC√3 = 90/BCBC = 90/√3 = 90√3/3= 30√3= 30 ×1.73= 51.9Hence the ship is 51.9 m away from light house.