How do you calculate the hypotenuse of a right triangle?

Answer

The old pythagorean theorem says, "the square of the hypotenuse is equal to the sum of the square of the other two sides."

What that means is, get an accurate measurement of the two angles that touch the right angle, square them and add them together then take the square root of that number and you'll have the length of the hypotenuse.

In mathematical terms it's:

A-squared + B-squared = C-squared. (sorry, I don't have a superscript key anywhere near)

The hypotenuse of a right angled triangle is the longest side, or the one opposite the right angle. It can be calculated using a variety of methods -

Pythagoras theorem : A² + B² = C², where A and B are the sides adjacent to the right angle, and C is the hypotenuse. The square of A plus the square of B is equal to the square of C, so C can be calculated as √(A² + B²).

Trigonometric angle rules : Sin(e) x = ^o/_h, cos(ine) x = ^a/_h, tan(gent) x = ^o/_a, where x is one of the other two angles, o is the side opposite this angle, a is the side adjacent to it, and h is the hypotenuse. Using these angle rules, you can calculate the length of any of the sides given the length of one of the other sides plus an angle.

There are others, but they start to become more difficult to explain without other knowledge in triangle geometry!

a²+b²=c<sup>2



/l
/ l
/ l
C / l A
/ l
/ l
/ l
/____ l

B</sup>

Example:

/l
/ l
/ l
C / l A=4
/ l
/ l
/ l
/___ l

B=3

a²+b²=c2
4²+3²=c²
16+9=c²
25=c²
square root of 25= square root of c²
5=c

Answer:
/l
/ l
/ l
C=5 / l A=4
/ l
/ l
/ l
/____ l

B=3

Formula:
a²+b²=c2

Example:
A=4
B=3
C=?

a²+b²=c2
4²+3²=c²
16+9=c²
25=c²
square root of 25= square root of c²
5=c

Answer:
A=4
B=3
C=5

First answer by Redbeard. Last edit by Redbeard. Contributor trust: 3105 [recommend contributor]. Question popularity: 27 [recommend question].