Question

The angle of elevation of the top of a tower at a point on the line through the foot of the tower is `45^@`. After walking a distance towards the foot of the tower along the same horizontal line elevation of the top of the tower changes to `60^@`. Find the height of tower.

Answer 1

With the given details, we can create a diagram.
Please refer to video to see the diagram.
From the digram,
In `Delta OBC`,
`h/x = tan60^@ = sqrt3`
`=>x = h/sqrt3->(1)`
In `Delta OAC`,
`h/(80+x) = tan45^@ = 1`
`=> h = 80+x`
From (1),
`=>h = 80+h/sqrt3`
`=>sqrt3h-h = 80sqrt3`
`=>h = (80sqrt3)/(sqrt3-1)**(sqrt3+1)/(sqrt3+1)`
`=>h = 40sqrt3(sqr3+1)m`
So,the height of the tower is `40sqrt3(sqrt3+1)m`.