Question

from a point p on the ground the angle of elevation of the top of a building is 30°and that of the flag staff fixed on the top of the building is 45°. if the length of the flag staff is 5m find the height of the building.​

Answer 1

Answer:

Step-by-step explanation:

Suppose the point p is x meter away from the building and the height of the building excluding the flagstaff is h meter

So tan 30 = h / x

tan 30 = h / x

1/√3 = h / x

x = h√3

Now tan 45 = ( h + 5 ) / x

tan 45 = ( h + 5 ) / x

1 = ( h + 5 ) / x

x = ( h + 5)

x = h + 5

We get x = h√3 and even h + 5

So we can consider that h√3 = h + 5

h√3 = h + 5

h√3 - h = 5

h ( √3 - 1 ) = 5

h ( 1.732 - 1 ) = 5        [ USING √3 = 1.732 ]

h ( 0.732 ) = 5

h = 5 / 0.732

h = 6.8306 m

So the height of the building is 6.8306 meter