Question

A length of rope is stretch between the top edge of the building at stake in the ground the head of the state is at ground level the rope also touches a tree that is growing halfway between the state and the building if the tree is 38 feet tall how tall is the building

Answer 1

Assuming the rope touches the top of the tree, then by similar triangles, the building must be 32 feet tall.

Hope this helps!

Answer 2

Height of building is 76 feet.

Explanation:

In the figure below,

AB is the building , DE is the tree standing in half way between the state and building.

Let angle at C be
`\theta`

In ΔABC,

tan
`\theta` =
`(\text Perpendicular)/(\text Base)`

tan
`\theta` =
`(h)/(2x)` ......(1)

In ΔDEC,

tan
`\theta` =
`(\text Perpendicular)/(\text Base)`

tan
`\theta` =
`(38)/(x)` ......(2)

Comparing (1) and (2) ,

`(h)/(2x)` =
`(38)/(x)`

`h=2*38`

⇒
`h=76`

Thus, Height of building is 76 feet.