Question

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

Answer 1

For this case what we must do is use the cosine theorem to solve the problem.
 We have then:
 $c ^ 2 = a ^ 2 + b ^ 2 - 2abcos (x)$
 Where,
 a, b, c: are the sides of the triangle.
 x: is the angle between the sides a and b of the triangle.
 Substituting values we have:
 $c ^ 2 = 90 ^ 2 + 75 ^ 2 - 2 (90) (75) cos (85)$
 Clearing c we have:
 $c = \sqrt{90 ^ 2 + 75 ^ 2 - 2 (90) (75) cos (85)}$
 Answer:
 option 1
 $c = \sqrt{90 ^ 2 + 75 ^ 2 - 2 (90) (75) cos (85)}$