Solve for the Pythagorean Theorem: "In a triangle rectangle the sum of the squares of the legs is equal to the square of the hypotenuse"
SOLVING:
1) \(8^{2} + b^{2} = 10^{2}\)
\(64 + b^{2} = 100\)
\(b^{2} = 100 - 64\)
\(b^{2} = 36\)
\(b = \sqrt{36}\)
\(\boxed{b = 6\:ft}\end{array}}\qquad\quad\checkmark\)
2) \(a^{2} + 24^{2} = 26^{2}\)
\(a^{2} + 576 = 676\)
\(a^{2} = 676 - 576\)
\(a^{2} = 100\)
\(a = \sqrt{100}\)
\(\boxed{a = 10\:in}\end{array}}\qquad\quad\checkmark\)
3) \(18^{2} + 15^{2} = c^{2}\)
\(324 + 225 = c^{2}\)
\(549 = c^{2}\)
\(c^{2} = 549\)
\(c = \sqrt{549}\)
\(\boxed{c \approx 23.4\:cm}\end{array}}\qquad\quad\checkmark\)
4) \(a^{2} + 14^{2} = 28^{2}\)
\(a^{2} + 196 = 784\)
\(a^{2} = 784 - 196\)
\(a^{2} = 588\)
\(a = \sqrt{588}\)
\(\boxed{a \approx 24.2\:yd}\end{array}}\qquad\quad\checkmark\)
5) \(50^{2} + 50^{2} = c^{2}\)
\(2500 + 2500 = c^{2}\)
\(5000 = c^{2}\)
\(c^{2} = 5000\)
\(c = \sqrt{5000}\)
\(\boxed{c \approx 70.7\:mm}\end{array}}\qquad\quad\checkmark\)
6) \(45^{2} + 64^{2} = c^{2}\)
\(2025 + 4096 = c^{2}\)
\(6121 = c^{2}\)
\(c^{2} = 6121\)
\(c = \sqrt{6121}\)
\(\boxed{c \approx 78.2\:m}\end{array}}\qquad\quad\checkmark\)
