### All High School Math Resources

## Example Questions

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

**Possible Answers:**

**Correct answer:**

### 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 ?

**Possible Answers:**

**Correct answer:**

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 #3 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

If angle , and , what is the value of ?

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

**Correct answer:**

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 :

**Possible Answers:**

**Correct answer:**

Solve for using the Pythagorean Theorem:

### Example Question #21 : Triangles

If and , how long is side ?

**Possible Answers:**

Not enough information to solve

**Correct answer:**

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

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

**Possible Answers:**

*π*

√10

√15

5

5√2

**Correct answer:**

5√2

Using the Pythagorean theorem, *x*^{2} + *y*^{2} = *h*^{2}. And since it is a 45-45-90 triangle the two short sides are equal. Therefore 5^{2} + 5^{2} = *h*^{2 }. Multiplied out 25 + 25 = *h*^{2}.

Therefore *h*^{2} = 50, so *h* = √50 = √2 * √25 or 5√2.

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

The lengths of the sides of a right triangle are consecutive odd numbers, and the length of the shortest side is x. Which of the following equations could be used to solve for x?

**Possible Answers:**

x^{2} + (x + 2)^{2} = (x + 4)^{2}

(x + 4)^{2} + x^{2} = (x + 2)^{2}

x = (x – 1) + (x – 2)

x^{2} = (x + 1)^{2} + (x + 2)

x^{2} = (x + 2)^{2} + (x + 4)^{2}

**Correct answer:**

x^{2} + (x + 2)^{2} = (x + 4)^{2}

Using the Pythagorean Theorem, a^{2 }+ b^{2} = c^{2}, we can substitute x for a. Consecutive odd integers are denoted as (x + 2), (x + 4), etc. Therefore, we substitute (x + 2) for b, and (x + 4) for c, resulting in x^{2} + (x + 2)^{2} = (x + 4)^{2}.

### Example Question #5 : 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?

**Possible Answers:**

√(43)/2

3π/4

√(34)

None of the other answers

4π/5

**Correct answer:**

√(34)

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^{2 }+ 5^{2 }= c^{2}. 34 = c^{2}, c = √(34).

### All High School Math Resources

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