Answer:
- 384 mph or 480 mph (see two solutions)
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Consider triangle AQP.
It has two known sides and the included angle:
- AQ = 4 mi;
- AP = 5 mi;
- m∠A = 80° - 40° = 40°.
Use the law of cosines to find the third side:
- QP² = AQ² + AP² - 2AQ*AP*cos A
- QP² = 4² + 5² - 2*4*5*cos 40°
- QP² = 10.35
- QP = √10.35
- QP = 3.2 mi
The distance traveled in 30 seconds is 3.2 miles, so the speed of the plane, in terms of mph is the distance travelled in 1 hour = 3600 sec:
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Note. There is another solution with different result. It means the question isn't perfect and confusing.
We found angle A above, or ∠QAP = 40°.
Also, we can see if PT║AT and AP is transversal, it gives us:
- ∠QPA ≅ ∠PAT as alternate interior angles
It means ΔAQP is isosceles, which means:
- AQ = QP = 4 mi, as opposite angles are same
It gives us the different speed: