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) [tex] 8^{2} + b^{2} = 10^{2} [/tex]
[tex]64 + b^{2} = 100[/tex]
[tex] b^{2} = 100 - 64[/tex]
[tex] b^{2} = 36[/tex]
[tex]b = \sqrt{36} [/tex]
[tex]\boxed{b = 6\:ft}\end{array}}\qquad\quad\checkmark[/tex]
2) [tex] a^{2} + 24^{2} = 26^{2} [/tex]
[tex] a^{2} + 576 = 676[/tex]
[tex] a^{2} = 676 - 576[/tex]
[tex] a^{2} = 100[/tex]
[tex]a = \sqrt{100} [/tex]
[tex]\boxed{a = 10\:in}\end{array}}\qquad\quad\checkmark[/tex]
3) [tex] 18^{2} + 15^{2} = c^{2} [/tex]
[tex]324 + 225 = c^{2} [/tex]
[tex]549 = c^{2} [/tex]
[tex] c^{2} = 549[/tex]
[tex] c = \sqrt{549} [/tex]
[tex]\boxed{c \approx 23.4\:cm}\end{array}}\qquad\quad\checkmark[/tex]
4) [tex] a^{2} + 14^{2} = 28^{2} [/tex]
[tex] a^{2} + 196 = 784[/tex]
[tex] a^{2} = 784 - 196[/tex]
[tex] a^{2} = 588[/tex]
[tex]a = \sqrt{588} [/tex]
[tex]\boxed{a \approx 24.2\:yd}\end{array}}\qquad\quad\checkmark[/tex]
5) [tex] 50^{2} + 50^{2} = c^{2} [/tex]
[tex]2500 + 2500 = c^{2} [/tex]
[tex]5000 = c^{2} [/tex]
[tex] c^{2} = 5000[/tex]
[tex]c = \sqrt{5000} [/tex]
[tex]\boxed{c \approx 70.7\:mm}\end{array}}\qquad\quad\checkmark[/tex]
6) [tex] 45^{2} + 64^{2} = c^{2} [/tex]
[tex]2025 + 4096 = c^{2} [/tex]
[tex]6121 = c^{2} [/tex]
[tex] c^{2} = 6121[/tex]
[tex]c = \sqrt{6121} [/tex]
[tex]\boxed{c \approx 78.2\:m}\end{array}}\qquad\quad\checkmark[/tex]
