Question

Find the length of a lake, CB, given the distances AB = 290 m and AC= 225 m and the angle  = 72°

Answer 1

To determine the length of the third side of the triangle, we will use the cosine law.

Recall that according to the cosine line, if we have two known sides and the angle between those sides we can compute the third side using the following formula:

`c=\sqrt[]{a^2+b^2-2ab\cos \gamma},`

where c is the missing side.

Substituting a=290, b=225, and γ=72° in the above formula we get:

`c=\sqrt[]{290^2+225^2-2\cdot290\cdot225\cdot\cos 72^(\circ)}.`

Simplifying the above result, we get:

`c\approx307.`

Answer:

`307.`