Question

If Peter is currently facing towards Skeleton Cove, how many degrees to his left should he turn before walking 673 paces to the treasure? Do not round during your calculations. Round your final answer to the nearest degree.

Answer 1

61.4 degrees is the angle.

Answer 2

Angle = 59⁰

Explanation:

First make a sketch of the situation. This results in a triangle.

Now, since there are three sides, the law of cosines is applicable here. This is because we have three sides but unknown angles.

The law of cosines is as follows:

(BC)² = (AB)² + (AC) ² -2AB·AC·Cos A

Making Cos A the subject of the equation gives:

Cos (A) = [(AB)² + (AC)²- (BC)²]/[2AB·AC]

Cos A = [(673)² + (989)² - (861)²]/ (2×673×989)

Cos A = 689 729/ (1331194)

A = Cos⁻¹ [689 729/ (1331194)]

= 58.8⁰

= 59⁰ (nearest degree)