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

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

$\textup{What is the length of the hypotenuse of a right triangle with legs of lengths 10 and 15?}$

Possible Answers:

$5\sqrt{13}$

$13\sqrt{5}$

$6\sqrt{13}$

Correct answer:

$5\sqrt{13}$

Explanation:

$\textup{Pythagorean Theorum: }a^{2}+b^{2}= c^{2}\;\;\;\;\;\;10^{2}+15^{2}=c^{2}$

$100+225=c^{2}\;\;\;\;325=c^{2}\;\;\;\;\;\sqrt{325}=c\;\;\;\;\sqrt{25}\times\sqrt{13}=c$

$5\sqrt{13}=c$

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

Rt_triangle_letters

If angle $c=90^\circ$ , Y=3 and Z=4 , what is the value of ?

Possible Answers:

12.5

Correct answer:

Explanation:

Once we see that $c=90^\circ$ , 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 ( a^2+b^2=c^2 ) or, in this case: Y^2+Z^2=X^2 .

Plug in our given values to solve:

Y^2+Z^2=X^2

3^2+4^2=X^2

9+16=X^2

25=X^2

$\sqrt{25}=\sqrt{X^2}$

5=X

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

Rt_triangle_letters

If angle $c=90^\circ$ , X = 13 and Y = 12 , what is the value of ?

Possible Answers:

169

144

17.69

Correct answer:

Explanation:

Once we see that $c=90^\circ$ , we know we're working with a right triangle and that will be the hypotenuse.

At this point we can use the Pythaogrean theorem ( a^2+b^2=c^2 ) or, in this case: Y^2+Z^2=X^2 .

Plug in our given values to solve:

Y^2+Z^2=X^2

12^2+Z^2=13^2

144+Z^2=169

Subtract 144 from both sides:

Z^2=25

$\sqrt{Z^2}=\sqrt{25}$

Z=5

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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:

$5\sqrt{2}$

$5\sqrt{5}$

$\sqrt{5}$

Correct answer:

$5\sqrt{2}$

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, a^2+b^2=c^2 .

Plug in our given values.

a^2+b^2=c^2

5^2+5^2=c^2

25+25=c^2

50=c^2

$\sqrt{50}=\sqrt{c^2}$

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

$\sqrt{25*2}=\sqrt{c^2}$

IS a perfect square, so we can simplify!

$\sqrt{25}*\sqrt{2}=\sqrt{c^2}$

$5*\sqrt2=c$

$5\sqrt{2}=c$

This is going to be true of all isoceles right triangles: the pattern will always be $x:x:x\sqrt{2}$ .

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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:

$4\sqrt{2}$

$2\sqrt{2}$

Correct answer:

$4\sqrt{2}$

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, a^2+b^2=c^2 .

Plug in our given values.

a^2+b^2=c^2

4^2+4^2=c^2

16+16=c^2

32=c^2

$\sqrt{32}=\sqrt{c^2}$

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

$\sqrt{16*2}=\sqrt{c^2}$

IS a perfect square, so we can simplify!

$\sqrt{16}*\sqrt{2}=\sqrt{c^2}$

$4*\sqrt2=c$

$4\sqrt{2}=c$

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

Solve for :

Question_12

Possible Answers:

x=9

$x=6\sqrt2$

x=12

$x=9\sqrt2$

Correct answer:

$x=6\sqrt2$

Explanation:

Solve for using the Pythagorean Theorem:

c^2=a^2+b^2

x=c

x^2=6^2+6^2=36+36=72

$\sqrt{x^2}=\sqrt{72}$

$x=\sqrt{36}\times \sqrt2$

$x=6\sqrt2$

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Example Question #81 : Geometry

Trig_id

If o=10ft and a=17ft , how long is side ?

Possible Answers:

Not enough information to solve

17.9ft

19.7 ft

18ft

19.3ft

Correct answer:

19.7 ft

Explanation:

This problem is solved using the Pythagorean theorem $(a^{2}+b^{2}=c^{2})$ . In this formula and are the legs of the right triangle while is the hypotenuse.

Using the labels of our triangle we have:

$o^{2}+a^{2}=h^{2}$

$\dpi{100} h^{2}=(10ft)^{2} +(17ft)^{2}$

$h^{2}=100ft^{2}+289ft^{2}$

$h=\sqrt{389ft^{2}}$

$\rightarrow 19.7 ft$

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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:

5√2

√10

√15

Correct answer:

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.

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Example Question #81 : Act Math

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

None of the other answers

4π/5

√(34)

Correct answer:

√(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 3²+ 5²= c². 34 = c², c = √(34).

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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?

Possible Answers:

Correct answer:

Explanation:

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

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

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

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

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

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

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

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

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

Example Question #81 : Geometry

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

Example Question #81 : Act Math

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

All High School Math Resources

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