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
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.
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
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.
