Question

A student walk 60m on a bearing of 028 degree and then 180m due east. How is she from her starting point, correct to the nearest whole number?

Answer 1

She is 215 m from the starting point

Explanation:

Let's begin by constructing a figurative representation of the information given (figure attached)

We know 2 sides of the triangle and the inner angle, we can therefore use the Cosine Rule

Mathematically represented as:

b² = a² + c² - 2ac(CosB)

b = ?, a = 60 m, c = 180, B = 118° (the sum of the 90° right angle at B + the interior angle of 28° from A)

b² = 60² + 180² - 2(60)(180)Cos 118°

b² = 3600 + 32400 - (- 10140.586)

b² = 46140.586 ⇒ b =
`√(46140.586)`

b = 214.8 m ≈ 215 m

b = 215 m (to the nearest whole number)

∴ the student is 215 m from the starting point