Help with a Distance problem.

Pat Cronin

New member
Joined
Oct 12, 2016
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I have this great math calendar which asks a different math question each day. The day of the week is the answer. The answer for the question today is 12 as today is 10/12/16.
The question is as follows:

The angle of depression of this airplane is 18 degrees to the airport.
If it's altitude is 21,120 feet, what's it's ground distance from the airport
to the nearest mile?

The formula I used was Sine(18) = 21,120/X; X being the distance to the airport. Simplifying the question, realizing 21,120 = 4 miles and Sine(18) = approx .31, I rewrote the formula as X = 4/.31.
This gave me 12.9, which I was looking for an answer between 11.6 and 12.4. What am I getting wrong here, just push me in the right direction.
Thanks,
Pat C.
 
I have this great math calendar which asks a different math question each day. The day of the week is the answer. The answer for the question today is 12 as today is 10/12/16.
The question is as follows:

The angle of depression of this airplane is 18 degrees to the airport.
If it's altitude is 21,120 feet, what's it's ground distance from the airport
to the nearest mile?

The formula I used was Sine(18) = 21,120/X; X being the distance to the airport. Simplifying the question, realizing 21,120 = 4 miles and Sine(18) = approx .31, I rewrote the formula as X = 4/.31.
This gave me 12.9, which I was looking for an answer between 11.6 and 12.4. What am I getting wrong here...?
You've been given the height (the vertical distance) and asked to find the ground distance (the horizontal distance). Sine uses the vertical ("opposite") and the hypotenuse (which is not horizontal). Are you sure you're using the sine ratio, and not, say, the tangent? Take a good look at your picture.... :wink:
 
Thanks for the Help

You've been given the height (the vertical distance) and asked to find the ground distance (the horizontal distance). Sine uses the vertical ("opposite") and the hypotenuse (which is not horizontal). Are you sure you're using the sine ratio, and not, say, the tangent? Take a good look at your picture.... :wink:

Sometimes in life you just need a little nudge in the right direction. This was one of those situations. I took a step back and solved the problem, Thanks. Pat C.
 
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