Question

PLEASE HELP ASAP!!!!!

You survey two oak trees across a narrow but deep gorge. The results of your survey are shown below.



Which expression below is equivalent to how many feet the oak trees are from each other?

the answer choices are the four expressions below.

Answer 1

Answer: sqrt 90^2+ 75^2- 2(90)(75) cos(85)

Answer 2

For this case what we must do is use the law of cosines.
We then have the following equation:

`c ^ 2 = a ^ 2 + b ^ 2 - 2 * a * b * cos (x)`
Where,
a, b: sides of the triangle
x: angle between sides a and b.
Substituting values we have:

`c^2 = 90^2 + 75^2 - 2*90*75*cos(85)`
Clearing the value of c we have:

`c = √( 90^2 + 75^2 - 2*90*75*cos(85))`
Answer:
An expression that is equivalent to how many feet the oak trees are from each other is:

`c = √( 90^2 + 75^2 - 2*90*75*cos(85))`