Question

english spanish 15 17 8 12 a 9 a² + 8² = 17² a = __ back next

Explanation:

Step1: Substitute values into Pythagorean theorem

We know the Pythagorean theorem for a right triangle is \(A^{2}+B^{2}=C^{2}\), here \(B = 8\) and \(C=17\). So we substitute these values into the formula: \(A^{2}+8^{2}=17^{2}\).

Step2: Calculate the squares

Calculate \(8^{2}=64\) and \(17^{2} = 289\). Then the equation becomes \(A^{2}+64=289\).

Step3: Solve for \(A^{2}\)

Subtract 64 from both sides of the equation: \(A^{2}=289 - 64\). So \(A^{2}=225\).

Step4: Find the value of \(A\)

Take the square root of both sides. Since \(A\) represents the length of a side of a triangle, we take the positive square root. \(\sqrt{A^{2}}=\sqrt{225}\), so \(A = 15\).

Answer:

15