[tex]\begin{gathered} Using\text{ pythagora's theory we have:} \\ \text{ (Hyp)}^{2\text{ }}=(opp)^2+(Adj)^2 \\ (20)^2=10^2+y^2 \\ 400\text{ = 100 + }y^2 \\ 400\text{ - 100 = }y^2 \\ y^2\text{ = 300} \\ y\text{ = }\sqrt[]{300\text{ }}\text{ = 17.3} \\ \\ \end{gathered}[/tex][tex]\begin{gathered} \text{from the diagram above we can also use pythagora's theory} \\ \text{ Z}^2=x^2+17.3^2\text{ --------------(1)} \\ \end{gathered}[/tex][tex]\text{Also from the main/ full diagram we have}\ldots[/tex][tex]\begin{gathered} using\text{ pythagora's Theaory we have.} \\ (x+10)^2=Z^2+20^2\text{ } \\ x^2\text{ + 20}x+100=Z^2\text{ + 400}-----------(2) \\ \text{substitue Z}^2\text{ in equation(1) into equation (2) which the becomes } \\ x^2\text{ + 20}x+100=Z^2\text{ + 400} \\ x^2\text{ + 20}x+100=x^2+17.3^2^{}\text{ + 400} \\ 20x\text{ = }17.3^2\text{ + 400 - 100} \\ 20x\text{ = 299.29 +300} \\ 20x\text{ = 599.29} \\ x\text{ =}\frac{599.29}{20}\text{ = 29.96} \end{gathered}[/tex][tex]\begin{gathered} using\text{ pythagora's theory too} \\ Z^2=29.96^2+17.3^2 \\ Z\text{ = 897.871 + 299.29} \\ Z^2\text{ = 1197.161} \\ Z\text{ =}\sqrt[]{1197.161}\text{ =34.6} \end{gathered}[/tex]
