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Masteriza [31]
2 years ago
10

This is confusing me please someone help

Mathematics
1 answer:
Viefleur [7K]2 years ago
4 0

Answer:

  • The distance from the plane to the observer tower is 7.7 km

Step-by-step explanation:

We are given two sides and one angle opposite to one of the known sides.

In order to find the missing side we need to use the law of sines.

<h3>Step 1</h3>

Find the angle opposite to the second known side, let it be x.

  • sin 68°/7.5 = sin x /5.2
  • sin x = 5.2 sin 68°/7.5
  • sin x = 0.64 (rounded)
  • x = arcsin 0.64
  • x = 39.8°

<h3>Step 2</h3>

Find the missing third angle y, using angle sum theorem:

  • 68° + 39.8° + y = 180°
  • 107.8° + y = 180°
  • y = 180° - 107.8°
  • y = 72.2°

<h3>Step 3</h3>

Find the required side length z, the distance from the plane to the observer tower, using the law of sines again.

<u>Note</u>. <em>At this point you can use the law of cosines as we have found the angle between the known sides.</em>

<em />

  • sin 68°/7.5 = sin 72.2°/z
  • z = 7.5 sin 72.2°/sin 68°
  • z = 7.7 km (rounded)

So the required distance is 7.7 km

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