## Calculate hypotenuse using sum of two sides and angles

Trigonometric ratios and functions, the unit circle, inverse trig functions, identities, trig graphs, etc.
gori
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Joined: Mon Jan 13, 2014 2:40 am
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### Calculate hypotenuse using sum of two sides and angles

Hi,

I am currently trying to work out the correct formula to the this problem.
Given a right angled triangle, where I know, all angles and the sum of hypotenuse+opposite sides what is the hypotenuse?

Example Problem:
Angles: A=54, B=36, C=90
hypotenuse+opposite=20 (adjacent side is unknown)
hypotenuse=?

Hope that is clear. I know given angle A there would be a ratio of the two sides in a right angled triangle, just don't know the formula to calculate it.

Thanks
Gori

gori
Posts: 2
Joined: Mon Jan 13, 2014 2:40 am
Contact:

### Re: Calculate hypotenuse using sum of two sides and angles

I have come up with one that works for me.
where i = hypotenuse+opposite

$\Large h=i\frac{1}{1+sin(A)}$

so for my example
$\Large 11.0557=20\frac{1}{1+sin(54)}$

little_dragon
Posts: 226
Joined: Mon Dec 08, 2008 5:18 pm
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### Re: Calculate hypotenuse using sum of two sides and angles

Given a right angled triangle, where I know, all angles and the sum of hypotenuse+opposite sides what is the hypotenuse?

Example Problem:
Angles: A=54, B=36, C=90
hypotenuse+opposite=20 (adjacent side is unknown)
hypotenuse=?
is "opposite" opposite A or B?
if A then a=20-h
sinA=a/h=(20-h)/h
plug in for sinA
solve for h

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