Question

Use the Pythagorean Theorem to write an equation to find the mission side of the triangle, then find the missing side. Round final answer to the nearest hundredth if necessary.

Answer 1

`\boxed{\sf x \approx 5.50}`

Explanation:

According to Pythagoras Theorem, "In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides"

`\therefore \\ \sf \implies x^(2) + 10.3^(2) = 11.7^(2) \\ \\ \sf 10.3 ^(2) = 106.09: \\ \sf \implies {x}^(2) + \boxed{106.09} = 11.7^(2) \\ \\ \sf 11.7^(2) = 138.89: \\ \sf \implies {x}^(2) + 106.09 = \boxed{138.89} \\ \\ \sf Subtracting \ 106.09 \ from \ both \ sides: \\ \sf \implies {x}^(2) = 138.89 - 106.09 \\ \\ \sf 138.89 - 106.09 = 30.8 \\ \sf \implies {x}^(2) = \boxed{30.8} \\ \\ \sf Taking \ square \ root \ of \ both \ sides: \\ \sf \implies x = √(30.8) \\ \\ √(30.8) = 5.5497: \\ \sf \implies x = \boxed{5.5497} \\ \\ \sf \implies x \approx 5.50`

Answer 2

x ≈ 5.50

Explanation:

`x^2=11.7^2-10.3^2`

`x^2=30.8`

`x=√(30.8)`

`x=5.4977477`

x ≈ 5.50