Type 1
this is a right triangle, the we can apply pythagoras
[tex]a^2+b^2=h^2[/tex]
where a and b are sides and h the hypotenuse on this case L(leash)
replacing
[tex]5^2+7^2=L^2[/tex]
simplify
[tex]\begin{gathered} 25+49=L^2 \\ 74=L^2 \end{gathered}[/tex]
now solve for L
[tex]L=\sqrt[]{74}\approx8.6[/tex]
The leash is 8.6ft
Type 2
we have a right triangle too
on this case the missing number is a side, not hypotenuse
remember pythagoras
[tex]a^2+b^2=h^2[/tex]
and replace for this case
[tex]x^2+19.5^2=20^2[/tex]
simplify
[tex]\begin{gathered} x^2+380.25=400 \\ \end{gathered}[/tex]
and solve for x
[tex]\begin{gathered} x^2=19.75 \\ x=\sqrt[]{19.75}\approx4.44 \\ \end{gathered}[/tex]
then le length of the side x is 4.44ft
