Question

A surveyor leaves her base camp and drives 42km on a bearing of 32 degrees. She then drives 25km on a bearing of 154 degrees. How far is she then from her base camp and what is her bearing from it

Answer 1

35.7 km and 248.3 °

Explanation:

I will attach the diagram to an image to make it easier to understand.

We will use the formula corresponding to the law of cosine

y² = 42² + 28² - (2 * 42 * 25 * cos 58 °)

y² = 2389 - 1112.83 = 1276.17

y = √1276.17

y = 35.72 km

Now, to calculate the surveyor's bearing from her base camp we must use the sine law:

[(Sin 58 °) / y] = [(Sin A) / 42]

Without A = (42 * without 58 °) /35.72

A = sin⁻¹ (0.9971)

A = 85.7 °

Bearing of the surveyor from the base camp = 270 ° - (85.7 ° - 64 °) = 248.3 °