Question

Draw a detailed diagram and use the Law of Sines to find the missing piece​

Answer 1

9514 1404 393

Answer:

1. insufficient information
2. 7.2 miles
3. 18.5 miles

Explanation:

1. Insufficient information. We need to know the direction of one observer from the other, and the reference for the angles being measured.

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2. See the first attachment. The law of sines tells you the distance r is ...

r = s(sin(R)/sin(S))

The angle at S is the supplement of the sum of the given angles:

∠S = 180° -35° -45° = 100°

Then the distance is ...

r = (10 mi)sin(45°)/sin(100°) = 7.1802 mi

The distance from Juan to the ship is about 7.2 miles.

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3. See the second attachment. The law of sines tells you the distance 'a' is ...

a = b(sin(A)/sin(B))

a = (10 mi)sin(45°)/sin(50°) ≈ 18.4612 mi

The distance from airplane B to the airport is about 18.5 miles.