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3 years ago

I need help with pythagoras’ theorem

Mathematics

1 answer:

fomenos3 years ago

4 0

Answer:

Pythagoras’ theorem is a way to find a side or hypothesis when you have 2 sides.

The formula is: a^2 + b^2 = c^2

a and b are sides

c is the hypothesis

Ex: A triangle has a leg that is 5 inches and a leg that is 7 inches. Find the hypothesis using Pythagoras' theorem.

A leg is another way of saying a side.

5^2 + 7^2 = c^2

25 + 49 = x^2

sqrt(74) = sqrt(x^2)

sqrt(74) inches = hypothesis

Ex: A triangle has a leg that is 9 feet and a hypothesis that is 25 feet. Find the other leg using Pythagoras' theorem.

9^2 + b^2 = 25^2

81 + b^2 - 81 = 625 - 81

sqrt(b^2) = sqrt(544)

b = sqrt(554)

Do you understand more?

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Write in simplest form: <img src="https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B24a%5E%7B10%7Db%5E%7B6%7D%7D" id="TexFormula1" ti

Charra [1.4K]

Answer:

$2a^3b^2\sqrt[3]{3a}$

Step-by-step explanation:

Use the following rules for exponents:

$a^m*a^n=a^{m+n}\\\\\sqrt[3]{x^3}=x$

Simplify 24. Find two factors of 24, one of which should be a perfect cube:

$8*3=24\\\\2^3=8$

Insert:

$\sqrt[3]{2^3*3a^{10}b^6}$

Now split the exponents. Split 10 into as many 3's as possible:

$10=3+3+3+1$

Insert as exponents:

$\sqrt[3]{2^3*3*a^3*a^3*a^3*a^1*b^6}$

Split 6 into as many 3's as possible:

$6=3+3$

Insert as exponents:

$\sqrt[3]{2^3*3*a^3*a^3*a^3*a^1*b^3*b^3}$

Now simplify. Any terms with an exponent of 3 will be moved out of the radical (rule #2):

$2\sqrt[3]{3*a^3*a^3*a^3*a^1*b^3*b^3}\\\\\\2*a*a*a\sqrt[3]{3*a^1*b^3*b^3}\\\\\\2*a*a*a*b*b\sqrt[3]{3*a^1}$

Simplify:

$2a^3b^2\sqrt[3]{3a}$

:Done

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A = 1/2 b h where b = 3.4 cm and h = 8 cm

A = 1/2 (3.4)(8)

A = 13.6 cm^2

Answer: 13.6 cm^2

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