SAT Math help » Geometry » plane Geometry » triangle » ideal Triangles » exactly how to discover the size of the hypotenuse of a ideal triangle : Pythagorean to organize

### Example question #1 : exactly how To find The size Of The Hypotenuse of A best Triangle : Pythagorean theorem If and , how long is side ?    Explanation:

This trouble is resolved using the Pythagorean theorem . In this formula and are the foot of the ideal triangle while is the hypotenuse.

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Using the labels of ours triangle we have:     ### Example question #2 : just how To discover The size Of The Hypotenuse the A right Triangle : Pythagorean organize

Explanation:

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

### Example concern #3 : how To find The size Of The Hypotenuse of A appropriate Triangle : Pythagorean to organize

The height of a best circular cylinder is 10 inches and also the diameter the its base is 6 inches. What is the street from a allude on the leaf of the base to the center of the whole cylinder?

Explanation:

The best thing come do here is to attract diagram and also draw the appropiate triangle for what is gift asked. It does not matter where you place your point on the base due to the fact that any suggest will develop the very same result. We know that the facility of the base of the cylinder is 3 inches away from the basic (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 appropriate triangle through a elevation of 5 inches and also a base of 3 inches. So utilizing the Pythagorean to organize 32 + 52 = c2. 34 = c2, c = √(34).

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### Example inquiry #4 : just how To find The length Of The Hypotenuse that A right Triangle : Pythagorean to organize

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

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

5

6

25

7

9

5

Explanation:

The correct answer is 5. The pythagorean theorem claims that a2 + b2 = c2. For this reason in this instance 32 + 42 = C2. Therefore C2 = 25 and C = 5. This is additionally an example of the usual 3-4-5 triangle.

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### Example concern #5 : just how To uncover The length Of The Hypotenuse of A best Triangle : Pythagorean to organize

The lengths the the 3 sides the a best triangle kind a collection of consecutive even integers as soon as arranged from least to greatest. If the 2nd largest side has actually a length of x, then which the the adhering to equations can be provided to fix for x?

(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

(x – 2)2 + x2 = (x + 2)2

Explanation:

We space told that the lengths type a collection of consecutive even integers. Because even integers are two units apart, the side lengths need to differ by two. In various other words, the largest side length is two higher than the second largest, and the 2nd largest size is two better than the smallest length.

The 2nd largest size is same to x. The 2nd largest size must therefore be two less than the largest length. We could represent the biggest length as x + 2.

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

To summarize, the lengths that the triangle (in regards to x) room x – 2, x, and also x + 2.

In order to fix for x, us can manipulate the fact that the triangle is a appropriate triangle. If we apply the Pythagorean Theorem, us can set up one equation that might be used to solve for x. The Pythagorean Theorem claims that if a and also b are the lengths that the legs of the triangle, and c is the size of the hypotenuse, then the adhering to is true:

a2 + b2 = c2

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