Question

the angle of elevation of the top of a tower from a certain points is 30°. if the observer moves 20 m towards the tower,the angle of elevation of the top of the tower increases by 15°. the height of the tower is

Answer 1

Let us suppose height of tower = x m and observer is standing y meter far from the foot of tower

Because angle of elevation is 30 degree

Tan (30)= Rise /Run = x/y

Now observer moves 20 meter towards the tower so distance between observer and foot of the tower is now y-20

Angle of elevation = previous angle + 15 = 30+15= 45 degree

Tan 45 = Rise /Run x/(y-20)

We know Tan 45 is equal to 1 so 1= x/( y-20) it becomes : y-20= x

Let us place this value of x in tan 30 = x/y

Tan 30 = (y-20)/y

multiply both sides by y

y * Tan 30 = y- 20

subtract y tan 30 and add 20 both sides

y- y tan 30 = 20

factor out y

y( 1- tan 30) = 20

divide both sides by 1-tan 30

y= 20 /( 1- tan 30 )

let us place value of tan 30

y= 20 /(1- 0.577)

Y= 20 /0.422

y= 47.39

Let us now find x by plugging this value of y

we have x= y-20 = 47.39- 20 = 27.39 meters

Answer : Height of tower = 27.39 meter