Question

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applying the pythagorean theorem
what is the value of x?
x =
(right triangle with legs x and 8, hypotenuse 10)

Explanation:

Step1: Recall Pythagorean Theorem

For a right triangle, \(a^2 + b^2 = c^2\), where \(c\) is the hypotenuse, and \(a, b\) are the legs. Here, hypotenuse \(c = 10\), one leg \(b = 8\), and the other leg is \(x\). So the formula becomes \(x^2 + 8^2 = 10^2\).

Step2: Solve for \(x^2\)

Calculate \(8^2 = 64\) and \(10^2 = 100\). Then \(x^2 = 100 - 64\). So \(x^2 = 36\).

Step3: Find \(x\)

Take the square root of both sides: \(x = \sqrt{36}\). Thus, \(x = 6\).

Answer:

\(x = 6\)