Answer:
1. Sails come in many shapes and sizes. Is the Sail on the right a right?
[tex](10.24)^2=(9.75)^2+(3.45)^2\\104.8576=95.0625+11.9025\\104.8576=106.965\\104.8576\neq 106.965[/tex]
No, it is not.
2.
Using the Pythagorean theory
[tex]20^{2}=a^{2} +b^{2} \\20=\sqrt{a^{2} +b^{2} }[/tex]
The possible values of the legs satisfy the equation above, where a and b are diffent from zero.
3.
The diagonal of a rectangular prism is: [tex]d^2=x^2+y^2+z^2[/tex]
[tex]d^2=3^2+4^2+8^2\\d^2=9+16+64\\d=\sqrt{89} \\d=9.43398\dots cm[/tex]
4.
The ladder lengh is 9 foot: triangle hypotenuse
Distance between the ladder base and bottom of tree is 4 feet: triangle leg
[tex]9^2=4^2+h^2\\81=16+h^2\\65=h^2\\h=\sqrt{65}\\\\h=8.062ft[/tex]
5.
[tex]d^2=4^2+8^2\\d^2=16+64\\d=\sqrt{80} \\d=8.94ft[/tex]
