Word problem (hypotenuse and triangles)

[devasquez10]

A tour bus is traveling along a triangular path. The three straight lines form a right triangle. One leg of the triangle represents a distance of 32 miles. The other leg of the triangle is 16 miles shorter than the hypotenuse. What is the length of the hypotenuse of this triangle? Of the other leg?

I am confused how I would set up this equation up or what formula to use. Do I use the a^2+b^2=c^2 method ?

 

[MarkFL]

Yes, the Pythagorean theorem is a good method to use here. Let's let \(x\) be the length of the hypotenuse in miles. Then, what will be the length of the unknown leg?

 

[devasquez10]

Would it be -16 because the other leg is 16 miles shorter than hypotenuse?

 

[MarkFL]

It would be:

[MATH]x-16[/MATH]
because we want to subtract 16 from whatever the hypotenuse is. Now, we can use the Pythagorean theorem to relate the 3 sides...what equation do you get?

 

[pka]

A tour bus is traveling along a triangular path. The three straight lines form a right triangle. One leg of the triangle represents a distance of 32 miles. The other leg of the triangle is 16 miles shorter than the hypotenuse. What is the length of the hypotenuse of this triangle? Of the other leg?

Notation: \(\displaystyle H,~G~\&~X\) are the names of the hypotenuse, the given side, and the other side. Let \(\displaystyle \|H\|\) stand for the length of side \(\displaystyle H\)
So lets assign the lengths: \(\displaystyle \|H\|=h.~\|G\|=32~\&~\|X\|=h-16\)
Can you solve this: \(\displaystyle h^2=(32)^2+(h-16)^2~?\)

 

[devasquez10]

This is how far I got
h^2=1024+h^2-256

 

[pka]

This is how far I got h^2=1024+h^2-256

It appears to me that you need to go back an review basic, basic algebra.
Can you solve this: \(\displaystyle h^2=(32)^2+(h-16)^2~?\\h^2=2^{10}+h^2-2^5h+2^8\\h=~?\)

Please look here.