SOLUTION: A plane passes directly over your head at an altitude of 500 feet. Two seconds later you observe that the angle of elevation to the plane is 42 degree. How far did the plane travel

Question 1076199: A plane passes directly over your head at an altitude of 500 feet. Two seconds later you observe that the angle of elevation to the plane is 42 degree. How far did the plane travel during those 2 seconds? How fast is the plane traveling in miles per hour?
Can someone help me with this? I am trying to use the tangent, but not sure.
Thank you.
Found 2 solutions by Boreal, MathTherapy:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
It is the tangent
tan 42=500/x, if height hasn't changed.
x=500/tan 42=555.31 feet
that is in 2 seconds, so in 1800*2 seconds or 1 hour, divided by 5280 ft/mile, the answer is 378.62 mph
check
60 mph is 88 ft/sec
360 mph is 528 ft/sec
This is comparable.
Answer by MathTherapy(10556) (Show Source): You can put this solution on YOUR website!
A plane passes directly over your head at an altitude of 500 feet. Two seconds later you observe that the angle of elevation to the plane is 42 degree. How far did the plane travel during those 2 seconds? How fast is the plane traveling in miles per hour?
Can someone help me with this? I am trying to use the tangent, but not sure.
Thank you.

You're using the correct trig ratio to find the distance traveled in 2 seconds.
The distance traveled in 2 seconds is:
Converting this speed (555.31 feet in 2 seconds), we get plane's speed as:
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