# Get size of cathetus/i from size of hypothenuse and also proportion in between catheti?

Just how can I compute the size of the cathetus in a triangular if I recognize the size of the hypotenuse and also the proportion in between both catheti?

As an example :

The hypotenuse is $5$cm long, and also the proportion in between the catheti is $4:3$ - how much time are the catheti or either cathetus?

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2019-05-07 10:38:26
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You can call one cathetus 4 *x *, the various other 3 *x *, and also use Pythagora's theory : (4 *x *) 2 +(3 *x *) 2 = 5 2 .

You will certainly get 25 *x * 2 = 25, which generates x = 1. So one cathetus is 4cm, and also the various other 3cm.

(Remember that 3,4,5 is a Pythagorean three-way)

0
2019-05-09 07:00:21
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Let the proportion be 1 :r and also the hypotenuse be h. After that the sides are after that x and also rx for some x. By the Pythagorean Theorem we get $x^2+r^2*x^2=h^2$. So $x=\sqrt{{h^2}/(1+r^2)}$. We can after that compute rx, the opposite side.

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2019-05-09 06:58:11
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