Question

Triangle solve for x, 3square root 2 & 5square root 2

Answer 1

`25)\text{ }x\text{ = 4 }\sqrt[]{2}`

Step-by-step explanation:

25) The triangle is a right angled traingle

To get the missing side (solve for x), we will apply pythagoras theorem:

Hypotenuse² = opposite² + adjacent²

hypotenuse = longest side or highest value = 5√2

let adjacent = x, opposite = 3√2

substitute the values into the formula above:

`\begin{gathered} (5\sqrt[]{2})^2\text{ = (3}\sqrt[]{2})^2+x^2 \\ 25(2)=9(2)+x^2 \\ 50=18+x^2 \\ 50-18=x^2 \\ 32=x^2 \end{gathered}`
`\begin{gathered} \text{square root both sides:} \\ \sqrt[]{32}=\sqrt[]{x^2\text{ }} \\ x\text{ = }\sqrt[]{32}\text{ = }\sqrt[]{16*2} \\ x\text{ = 4}\sqrt[]{2} \end{gathered}`