### Example question #1 : just how To uncover The size Of The Hypotenuse that A right Triangle : Pythagorean theorem

If

and , just how long is side ?Explanation:

This trouble is solved using the Pythagorean theorem

. In this formula and are the legs of the ideal triangle while is the hypotenuse.You are watching: Find the length of the hypotenuse of a right triangle whose legs are 3 and .

Using the labels of ours triangle we have:

### Example inquiry #1 : how To uncover The size Of The Hypotenuse the A best Triangle : Pythagorean to organize

Explanation:

Therefore *h*2 = 50, for this reason *h* = √50 = √2 * √25 or 5√2.

### Example question #1 : how To discover The length Of The Hypotenuse of A appropriate Triangle : Pythagorean theorem

The height of a ideal circular cylinder is 10 inches and also the diameter that its basic is 6 inches. What is the street from a point on the leaf of the basic to the center of the whole cylinder?

Explanation:

The ideal thing come do right here is to draw diagram and draw the appropiate triangle for what is gift asked. It does not matter where you ar your suggest on the base due to the fact that any allude will create the exact same result. We recognize that the facility of the basic of the cylinder is 3 inches far from the basic (6/2). We likewise know that the center of the cylinder is 5 inches native the base of the cylinder (10/2). Therefore we have a right triangle through a height of 5 inches and a basic of 3 inches. So making use of the Pythagorean organize 32 + 52 = c2. 34 = c2, c = √(34).

See more: What Is The Difference Between Inter And Intramolecular Forces ?

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### Example inquiry #4 : how To discover The size Of The Hypotenuse the A best Triangle : Pythagorean organize

A appropriate triangle with sides A, B, C and also respective angle a, b, c has actually the complying with measurements.

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

**Possible Answers:**

5

6

25

7

9

**Correct answer:**

5

Explanation:

The exactly answer is 5. The pythagorean theorem states that a2 + b2 = c2. So in this instance 32 + 42 = C2. So C2 = 25 and also C = 5. This is likewise an instance of the typical 3-4-5 triangle.

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### Example concern #5 : just how To uncover The length Of The Hypotenuse the A ideal Triangle : Pythagorean theorem

The lengths of the three sides the a best triangle type a collection of consecutive also integers once arranged from least to greatest. If the second largest side has a size of x, climate which the the following equations could be used to solve for x?

**Possible Answers:**

(x – 2)2 + x2 = (x + 2)2

(x – 2) + x = (x + 2)

x 2 + (x + 2)2 = (x + 4)2

(x – 1)2 + x2 = (x + 1)2

(x + 2)2 + (x – 2)2 = x2

**Correct answer:**

(x – 2)2 + x2 = (x + 2)2

Explanation:

We room told the the lengths type a series of consecutive even integers. Because even integers space two systems apart, the next lengths have to differ by two. In various other words, the biggest side size is two greater than the 2nd largest, and also the second largest size is two better than the smallest length.

The second largest size is equal to x. The second largest length must therefore be two less than the biggest length. We might represent the biggest length together x + 2.

Similarly, the 2nd largest size is two larger than the the smallest length, i m sorry we can thus represent as x – 2.

To summarize, the lengths that the triangle (in terms of x) space x – 2, x, and x + 2.

In order to settle for x, us can exploit the reality that the triangle is a appropriate triangle. If we use the Pythagorean Theorem, we can set up one equation that could be used to settle for x. The Pythagorean Theorem claims that if a and also b are the lengths that the foot of the triangle, and c is the length of the hypotenuse, climate the following is true:

a2 + b2 = c2

In this specific case, the 2 legs of our triangle space x – 2 and also x, due to the fact that the legs space the 2 smallest sides; therefore, we can say the a = x – 2, and b = x. Lastly, we deserve to say c = x + 2, since x + 2 is the size of the hypotenuse. Subsituting these values for a, b, and c into the Pythagorean Theorem returns the following: