# High School Math : How to find the length of the hypotenuse of a right triangle : Pythagorean Theorem

## Example Questions

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Explanation:

### Example Question #2 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

If angle  and , what is the value of ?

Explanation:

Once we see that , we know that we're working with a right triangle and that  will be the hypotenuse.

At this point we can use the Pythaogrean theorem () or, in this case: .

Plug in our given values to solve:

### Example Question #1 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

If angle  and , what is the value of ?

Explanation:

Once we see that , we know we're working with a right triangle and that  will be the hypotenuse.

At this point we can use the Pythaogrean theorem () or, in this case: .

Plug in our given values to solve:

Subtract  from both sides:

### Example Question #4 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

A right triangle has legs of  and . What is the hypotenuse?

Explanation:

To solve this problem, use the Pythagorean theorem: the sum of the square of the legs equals the square of the hyoptenuse or, mathematically, .

Plug in our given values.

is not a perfect square, but let's see if we can find a factor that is a perfect square.

IS a perfect square, so we can simplify!

This is going to be true of all isoceles right triangles: the pattern will always be .

### Example Question #5 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

A right triangle has legs of  and . What is the hypotenuse?

Explanation:

To solve this problem, use the Pythagorean theorem: the sum of the square of the legs equals the square of the hyoptenuse or, mathematically, .

Plug in our given values.

is not a perfect square, but let's see if we can find a factor that is a perfect square.

IS a perfect square, so we can simplify!

### Example Question #6 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Solve for :

Explanation:

Solve for  using the Pythagorean Theorem:

### Example Question #1 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

If  and , how long is side ?

Not enough information to solve

Explanation:

This problem is solved using the Pythagorean theorem  .  In this formula  and  are the legs of the right triangle while  is the hypotenuse.

Using the labels of our triangle we have:

### Example Question #1211 : Plane Geometry

If one of the short sides of a 45-45-90 triangle equals 5, how long is the hypotenuse?

√10

5

5√2

√15

π

5√2

Explanation:

Using the Pythagorean theorem, x2 + y2 = h2. And since it is a 45-45-90 triangle the two short sides are equal. Therefore 52 + 52 = h2 .  Multiplied out 25 + 25 = h2.

Therefore h2 = 50, so h = √50 = √2 * √25 or 5√2.

### Example Question #1 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

The height of a right circular cylinder is 10 inches and the diameter of its base is 6 inches. What is the distance from a point on the edge of the base to the center of the entire cylinder?

4π/5

None of the other answers

3π/4

√(43)/2

√(34)

√(34)

Explanation:

The best thing to do here is to draw diagram and draw the appropiate triangle for what is being asked. It does not matter where you place your point on the base because any point will produce the same result.  We know that the center of the base of the cylinder is 3 inches away from the base (6/2). We also know that the center of the cylinder is 5 inches from the base of the cylinder (10/2). So we have a right triangle with a height of 5 inches and a base of 3 inches. So using the Pythagorean Theorem 3+ 5= c2. 34 = c2, c = √(34).

### Example Question #1 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

A right triangle with sides A, B, C and respective angles a, b, c has the following measurements.

Side A = 3in. Side B = 4in. What is the length of side C?

7

25

9

6

5