Question

A plane flies from base camp to lake a, 205 km away in the direction 20.0° north of east. after dropping off supplies it flies to lake b, which is 175 km at 30.0° west of north from lake

a. determine the distance and direction from lake b to the base camp.

Answer 1

Draw a diagram to illustrate the problem as shown in the figure below.

Camp A is 20° north of east from the camp, therefore
m∠CAB = 80°
where C => base camp.

Let d = distance from lake B to the base camp, at x° west of south.
Apply the Law of Cosines to determine d.
d² = 205² + 175² - 2*205*175*cos80⁰
= 6.0191 x 10⁴
d = 245.338 km

Apply the Law of Sines to obtain

`(sin(x+30))/(205)= (sin80^(o))/(245.338)\\ \\ sin(x+30)=( (205)/(245.338))sin80^(o)= 0.8229`
x+30 = sin⁻¹ 0.8229 = 55.4°
x = 25.4°

Answer:
The distance from lake B to base camp is 243.3km (nearest tenth).
The direction is 25.4° west of south.