Question

You walk 53m to the north, then turn 30 degrees to your right and walk another 45m. How far are you from where you orginally started?

Answer 1

94.7m

Explanation:

Using the Law of Cosines this is easy to calculate. If you set your initial path as “side b” (From apex A to C) and the second path as “side a” (From apex C to B), then the distance from your origin is “side c” (From apex A to B) and is calculated from the Law of Cosines equation as:

`c^2 = a^2 + b^2 – 2*a*b*cos(gamma)`.

BUT remember that a “turn to the right” of 30’ means that angle for the equation is (180 – 30) = 150! (that just makes the cos value negative, but that is very important for the calculated value)

`c^2 = 45^2 + 53^2 – 2*45*53*cos(150)`.
`c^2 = 2025 + 2809 – 4770*(-0.866)`.
`c^2 = 8964.8` : `c^2 = 94.7m`