Question

Two searchlights on the shore of a lake are located 3020 yd apart. A ship in distress is spotted from each searchlight. The beam from the first searchlight makes an angle of 38 degrees with the baseline. The beam from the second light makes an angle of 57 degrees with the baseline. Find the ship's distance from each searchlight.

Answer 1

x₁ = 1866.2 yd distance between ship and searchlight in C

x₂ = 2542.5 yd . distance between ship and searchlight in B

Explanation:

The ship (point A) and the two searchlights points ( B and C) shape a triangle.

We have α = 38° ( opposite side x₁ or distance between ship and point C and β = 57 ° ( opposite side x₂ or distance between ship and point B then γ = 180 - ( α + β )

γ = 85°

Applying sin´slaw

x₁ / sin 38 = x₂/ sin57 = 3020 / sin 85

from sin table we find:

sin 38 = 0.6156

sin 57 = 0.8387

sin 85 = 0.9962

Then

x₁ / 0.6156 = 3020 / 0.9962

x₁ ( the opposite side to angle 38° ) / 0.6156 = 3031.5

x₁ = 3031.5*0.6156

x₁ = 1866.2 yd

x₂ = 3031.5 * 0.8387

x₂ = 2542.5 yd