Question

Use the Pythagorean theorem to find the third side of the triangle.​

Answer 1

`\huge\boxed{2√(21)\approx9.17}`

Explanation:

`\text{The Pythagorean theorem:}\\\\leg^2+leg^2=hypotenuse^2\\\\\text{We have:}\\\\leg=4,\ hypotenuse=10\\\\\text{Substitute:}\\\\4^2+leg^2=10^2\\\\16+leg^2=100\qquad\text{subtract 16 from both sides}\\\\16-16+leg^2=100-16\\\\leg^2=84\to leg=√(84)\\\\leg=√((4)(21))\qquad\text{use}\ √(ab)=√(a)\cdot√(b)\\\\leg=\sqrt4\cdot√(21)\\\\leg=2√(21)`

Answer 2

9.2 (1DP)

Explanation:

1. First you do 10^2 which is 10 X 10 = 100
2. Then you do 4^2 which is 4 X 4 = 16
3. Then you do 100 - 16. The way Ive learnt it is that if the hypotenuse isn't the one you have to find then minus of it it is then plus. So 100 - 16 = 84
4. A^2 + B^2 = C^2 84 is C^2 meaning now you have to square root it
5. Square root of 84 is 9.2 to 1 DP