Question

The angles of elevation and depression of the top and bottom of a tower from the top of a building, 60 m high are 30 degree and 60 degree respectively. Find the difference between the heights of the building and the tower and the distance between them.

Answer 1

Answer:20m

Step-by-step explanation:

height of tower = EC.

elevation angle,  = 60°

depression angle,  = 30°

we have to find , difference between the height of building and tower e.g., ED.

from ∆DAE,

or, tan30° = ED/AD

or, 1/√3 = ED/AD => AD = √3ED .....(1)

from ∆ABC,

or, tan60° = AB/CB

or, √3 = 60/AD [ from figure , AD = CB ]

or, √3AD = 60

from equation (1),

√3 × √3 ED = 60

or, 3ED = 60 => ED = 20m

Answer 2

Answer:20m

Step-by-step explanation:

height of tower = EC.

elevation angle,  = 60°

depression angle,  = 30°

we have to find , difference between the height of building and tower e.g., ED.

from ∆DAE,

or, tan30° = ED/AD

or, 1/√3 = ED/AD => AD = √3ED .....(1)

from ∆ABC,

or, tan60° = AB/CB

or, √3 = 60/AD [ from figure , AD = CB ]

or, √3AD = 60

from equation (1),

√3 × √3 ED = 60

or, 3ED = 60 => ED = 20m