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.
Step 1
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°
Step 2
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°
Step 3
Find the required side length z, the distance from the plane to the observer tower, using the law of sines again.
Note. At this point you can use the law of cosines as we have found the angle between the known sides.
- 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
