Question

A plane flies from base camp to lake A, a distance of 280 km at a direction of 20 degrees north of east. After dropping off supplies, the plane flies to lake B, which is 190km and 30 degree west of north from lake A.

Answer 1

Analyzing the diagram

Let $x=$ the distance between Base Camp and Lake B

Angle $\beta°=180-(70+30)$

$=80°$

Using cosine rule

$x^2=190^2+280^2-2×190×180\>Cos\>80$

$x=309.88km$

Using Sine Rule

$\frac{309.88}{Sin80}=\frac{280}{Sin({\theta}+30)}$

Sin $(\theta+30)=0.8898$

$\theta=32.85$

To return to Base the plan flies $309.88km$ at a direction of $32.85°$ west of south from Lake B