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 = √(90 ^ 2 + 75 ^ 2 - 2 (90) (75) cos (85))`
Answer:
option 1

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