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March 18th, 2015, 03:16 PM   #1
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Right Triangle Driving me mad

So I have a problem driving me crazy. There is a right triangle. Side B is given, it is 13.5. Side A and C are not given, nor are any angles besides the right angle. The only other information I am given is that side C is three times side A. So, if you multiplied side A by three, you would get side C, the hypotenuse. What formula do I use to solve this?? I drew a picture to help people understand.

http://puu.sh/gG2Z3/ef4f7df2a7.jpg
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March 18th, 2015, 03:21 PM   #2
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Math Focus: Calculus/ODEs
Use the Pythagorean theorem as follows:

$\displaystyle A^2+B^2=(3A)^2$

$\displaystyle A^2+B^2=9A^2$

$\displaystyle 8A^2=B^2$

$\displaystyle A^2=\frac{B^2}{8}$

$\displaystyle A=\frac{B}{2\sqrt{2}}$

Since you know $B$, you now know $A$ and $C=3A$.
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March 18th, 2015, 03:28 PM   #3
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I don't understand it completely, could you explain it a bit more please?

Where did the 8 come from in the third line, would I substitute 8 for the 13.5?
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March 18th, 2015, 03:35 PM   #4
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Math Focus: Calculus/ODEs
After squaring $3A$ in the right side, we have:

$\displaystyle A^2+B^2=9A^2$

Now, subtract $A^2$ from both sides to get:

$\displaystyle A^2-A^2+B^2=9A^2-A^2$

$\displaystyle B^2=8A^2$

Divide both sides by $8$:

$\displaystyle \frac{B^2}{8}=\frac{8A^2}{8}$

$\displaystyle \frac{B^2}{8}=\frac{\cancel{8}A^2}{\cancel{8}}$

$\displaystyle \frac{B^2}{8}=A^2$

If $a=b$ then $b=a$ so reverse sides to put the variable for which we are solving on the left:

$\displaystyle A^2=\frac{B^2}{8}$

Take the square root of both sides, and discard the negative root since all quantities represent measures of the sides of a triangle:

$\displaystyle \sqrt{A^2}=\sqrt{\frac{B^2}{8}}$

$\displaystyle A=\frac{\sqrt{B^2}}{\sqrt{8}}$

$\displaystyle A=\frac{B}{\sqrt{2^2\cdot2}}$

$\displaystyle A=\frac{B}{\sqrt{2^2}\cdot\sqrt{2}}$

$\displaystyle A=\frac{B}{2\sqrt{2}}$

Now, to find $A$, plug in the value of $B$, and then to get $C$, multiply $A$ by $3$.
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March 18th, 2015, 03:52 PM   #5
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Oh ok, I get it! Thank you very much. It turns out the answer they put was wrong, haha. They said it was 4.6 when in fact it was 4.77... Thanks!
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