Question

from a point A the angle of elevation of the top of vertical tower situated on the roof of 50m high building is found to be theta .after walking some distance towards the tower the angle of elevation of bottom of tower from point B is also theta.find the height of tower.

Answer 1

Answer:

Height of tower = 50 * (distance covered)/ (distance remained to Tower)

Step-by-step explanation:

from a point A the angle of elevation of the top of vertical tower situated on the roof of 50m high building is found to be theta .after walking some distance towards the tower the angle of elevation of bottom of tower from point B is also theta.find the height of tower.

Let Say x = height of tower

Building height = 50 m

Let say base of Building = O

then distance of point A = OA

distance of point B = OB

Tan Thetha = (50+x)/OA

Tan Thetha = 50/OB

=> (50+x)/OA = 50/OB

=> 50 OB  + x OB = 50 OA

=> x OB = 50 (OA - OB)

=> x = 50 AB / OB

Height of tower = 50 * (distance covered)/ (distance remained to Tower)

Answer 2

Answer:

Distance = 30 m and height = 10√3 m

Step-by-step explanation:

From ΔABC:

tan (θ) = opp/adj

tan (30) = BC/AB

BC = AB tan (30)

From ΔBCD:

tan (θ) = opp/adj

tan (60) = BC/BD

BC = BD tan (60)

Equate the 2 equations:

AB tan (60) = BD tan (30)

Define x:

Let BD = x

AB = x + 20

Solve x:

AB tan (30) = BD tan (60)

(x + 20) tan (30) = x tan (60)

x tan (30) + 20 tan (30) = x tan (60)

x tan (60) - x tan (30) = 20 tan (30)

x ( tan (60) - tan (30) ) = 20 tan (30)

x = 20 tan (30) ÷ ( tan (60) - tan (60) )

x = 10 m

Find the distance:

Distance = 10 + 20 = 30 m

Find the height:

tan (θ) = opp/adj

tan (60) = BC/10

BC = 10 tan (60)  = 10√3 m