Height And Distance

Height and Distance in just 10 second

Q .From the top of a cliff 88 m heigh , the angle of depression of the top and bottom of a tower observe to be 30° and 45° respectively. what is the height of tower.



Height of a cliff AB = 88m
∠DAF = 30° so ∠ADE = 30°
∠ACB = 45° so ∠DAF = 45°
so we have to calculate height of the tower CD =?

So in △ABC according to basic concept-


AB : BC : CA = 1 : 1 : √2

AB = 1 part = 88m = BC

BC = 88 = ED

Now in △ADE according to basic concept-


AB : BC : CA = 1 : √3 : 2

ED = √3 part = 88

AE = 1 part = 88m / √3

AE = 88/ √3 * √3 / √3

AE = 50.746666666667

Height of the tower CD = BE = BA - EA
CD = 88 - 50.746666666667
CD = 37.253333333333

So height of the tower is 37.253333333333.