# Applying Pythagoras backwards (with minimal information)

Discussion in 'Geometry and Trigonometry' started by NoviceBM, May 31, 2022.

1. ### NoviceBM

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Hello all!

While working on a personal project, I encountered the following math problem. I have a triangle with sides A, B, and C. I know the length of C = 15,3. Furthermore, I know that B / A = 7, so I can conclude that B = 7A. The triangle is a right angled triangle. To illustrate the problem, I have uploaded a visual representation attached to this post.

My goal is to know the lengths of sides A and B.

Is it possible to calculate those, and if so, how? It seems like a simple problem to solve with Pythagoras, but it's been years since I last touched any formulas. I've been breaking my head over it for the past few hours and just can't seem to get a (correct) answer. Do I need more information to calculate this? Any help would be greatly appreciated!

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NoviceBM, May 31, 2022
2. ### MathLover1

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so, c^2=a^2+b^2

if given:
c = 15,3
b / a = 7=> b = 7a

we have

15.3^2=a^2+(7a)^2........solve for a
15.3^2=a^2+49a^2
15.3^2=50a^2
15.3^2/50=a^2
a=sqrt(15.3^2/50)
a=15.3/sqrt(50)
a=2.1637467504308354

b = 7a =>b = 7*2.1637467504308354=15.1462272530158478

exact solution:
a=2.1637467504308354
15.1462272530158478

we can round it to one decimal place, so sides a and b are:
a=2.2 and b=15.2

MathLover1, May 31, 2022
NoviceBM and nycmathguy like this.
3. ### nycmathguy

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Very nice.

nycmathguy, May 31, 2022
4. ### NoviceBM

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Thank you so much! This is a very clear explanation.

I tried replicating the process with some different C and B/A values to see if I understood what was happening, and now I consistently managed to solve the equation. Turns out I did something wrong squaring my combined A and B values previously, which messed up the formula. Much appreciated!

NoviceBM, Jun 1, 2022
5. ### MathLover1

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when doing that kind of problems, make sure to recognize what is hypothenuse, what are legs, and which one is to find
formula you need is: c^2=a^2+b^2 where c is hypothenuse, a and b are legs

it means

the biggest square has the exact same area as the other two squares put together

an example:

Let's check if the areas are the same:

3^2 + 4^2 = 5^2

Calculating this becomes:

9 + 16 = 25

25=25

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Last edited: Jun 1, 2022
MathLover1, Jun 1, 2022
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