What is the square root of the hypotenuse?

Answer 1

The square root of a hypotenuse changes for every right triangle.

As you probably already know, a right triangle's angles are:

(leg)^2 + (other leg)^2 = (hypotenuse)^2

Or,

A^2 + B^2 = C^2

A & B are the two legs, and the C is the hypotenuse.

Since the hypotenuse changes for every triangle, you could have a triangle like this:

If A = 3, B = 4, and C = 5, then:

A^2 + B^2 = C^2

3^2 + 4^2 = 5^2

9 + 16 = 25

25 = 25

If you are trying to find the square root, it could look something like this:

If triangle ABC is a right triangle, and A = 3, and B = 4, find the hypotenuse C.

A^2 + B^2 = C^2

3^2 + 4^2 = C^2

9 + 16 = C^2

25 = C^2

sqrt (square root) 25 = sqrt C^2

5 = C

The square root of a square is a normal number. Sqrt 25^2 = 25, because the sqrt and the ^2 cancel each other out.

If you are trying to find a LEG, and are given another leg and the hypotenuse, then it could be something like this:

Triangle ABC is a right triangle. Find B. A = 3 and C = 5

To do this, you must isolate (get it alone on one side of the equal sign) the variable you are not given, like this:

A^2 + B^2 = C^2

3^2 + B^2 = 5^2

9 + B^2 = 25

(subtraction property of equality)

B^2 = 16

sqrt B^2 = sqrt 16

B = 4

As you can see, it is different for every triangle. You just have to figure it out. If you are allowed to use one, most calculators have a square root symbol on it.

There' s not much else to it. You just have to look at every triangle and find out what each individual angle is based on the information provided.