help please ive tried with my friends and no luck

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04-07-2022
Mathematics

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help please ive tried with my friends and no luck

Sagot :

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semsee45 semsee45 · Answer 1 · 2022-07-04T02:32:53-04:00

Answer:

[tex]a=5 \sqrt{7}[/tex]

Step-by-step explanation:

Pythagoras Theorem explains the relationship between the three sides of a right triangle. The square of the hypotenuse (longest side) is equal to the sum of the squares of the legs of a right triangle:

[tex]a^2+b^2=c^2[/tex]

where:

a and b are the legs of the right triangle
c is the hypotenuse (longest side) of the right triangle

Given:

b = 9
c = 16

Substitute the given values into the formula and solve for a:

[tex]\begin{aligned}a^2+b^2 & = c^2 \\\implies a^2+9^2 & =16^2\\a^2+81 & =256\\a^2+81-81 & =256-81\\a^2 & =175\\\sqrt{a^2} & =\sqrt{175}\\a & =\sqrt{25 \cdot 7}\\& = \sqrt{25}\sqrt{7}\\& =5\sqrt{7}\end{aligned}[/tex]

Therefore, the measure of the third side of the given right triangle is [tex]5 \sqrt{7}[/tex]

Learn more about Pythagoras Theorem here:

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Sagot :

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