Question

SMART PEOPLE ALERT!!!

Maria is standing next to a tree. The tree cast a shadow that is 5.4 ft long. Maria's shadow is 2.25 ft long. The angle formed from the sun hitting the tree and Maria are the same.

Maria is 5 ft tall.

How tall is the tree?

Answer 1

Finding the size of angle θ using the Trigonometry ratio

Tan θ =
`(opposite)/(adjacent)` =
`(5)/(2.25)` = 2.222...
θ =
`Tan^(2)(2.2222....)` = 65.8 (one decimal place)

Then using the value of θ to find the height of the tree
Tan θ =
`(oppoaite)/(5.4)`
2.22... =
`(x)/(5.4)`

`x=12` feet