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
