SOLUTION: Two mountain peaks are known to be 25 miles apart. A person located at a vista point, such that a right angle is spanned when he looks from one peak to the other, is told that the

Question 1074679: Two mountain peaks are known to be 25 miles apart. A person located at a vista point, such that a right angle is spanned when he looks from one peak to the other, is told that the distances from the vista point to each peak differ by 5 miles. How far is the vista point from each mountain peak?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
It helps to draw this.
The person is looking at each peak on a leg of a right triangle. The hypotenuse is the distance between the mountains.
x^2+(x+5)^2=25^2
x^2+x^2+10x+25=625
2x^2+10x-600=0
x^2+5x-300=0
(x+20)(x-15)=0
only positive root is x=15
x+5=20
The vista point is 15 miles from one mountain peak and 20 miles from the other.
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