Question

35 which of the following correctly uses the pythagorean theorem to find (image of a right triangle with hypotenuse 10, one leg 8, the other leg x) a $8^2 + (10)^2 = x^2$ b $x + 8 = 10$ c $x^2 + 8^2 = (10)^2$ d $x^2 + (10)^2 = 8^2$

Explanation:

Step1: Recall Pythagorean Theorem

The Pythagorean Theorem states that for a right - triangle with legs of lengths \(a\) and \(b\) and hypotenuse of length \(c\), \(a^{2}+b^{2}=c^{2}\).
In the given right - triangle, the hypotenuse is the side opposite the right angle. Here, the hypotenuse has length \(10\), and the two legs have lengths \(x\) and \(8\).

Step2: Apply the Theorem

Let \(a = x\), \(b = 8\) and \(c = 10\). Substituting these values into the Pythagorean Theorem \(a^{2}+b^{2}=c^{2}\), we get \(x^{2}+8^{2}=10^{2}\) (or \(x^{2}+8^{2}=(10)^{2}\)).

Answer:

C. \(x^{2}+8^{2}=(10)^{2}\)