Question

a zoologist hides in a bush 200 feet away from a tree inhabited by a family of monkeys. if the zoologist is looking up at an angle.of 15°, how high in the tree ate monkeys?

Answer 1

`\displaystyle 53.6ft`

Explanation:

refer the attachment

let the height be h

since we are given the adjacent side and want to figure out opposite side we'll use tan function

so our equation is

`\displaystyle \tan( {15}^( \circ) ) = (h)/(200)`

cross multiplication:

`\displaystyle h = 200\tan( {15}^( \circ) )`

by using calculator we acquire:

`\displaystyle h \approx 53.6ft`

hence,

about 53.6ft high in the tree ate monkeys