Answer:
a = 664.5
b = 502.3
c = 767.3
Step-by-step explanation:
Well, there are a couple of theorems that will help us do this problem
1. Given a right triangle and altitude to the hypotenuse, then the altitude is the mean proportion between the segments of the hypotenuse. That means in your problem that
[tex]\frac{435}{b} = \frac{b}{580}[/tex]
[tex]b^{2} = 435(580) = 252300\\b = \sqrt{252300} \\b = 502.3[/tex]
2. A leg of the triangle is the mean proportional between the hypotenuse and the segment adjacent to the leg. That means in your problem that
[tex]\frac{(435 + 580)}{c} = \frac{c}{580} \\c^{2} = 1015(580) = 588700\\c = \sqrt{588700} \\c = 767.3[/tex]
[tex]\frac{1015}{a} = \frac{a}{435} \\a^{2} = 1015(435) = 441525\\a = \sqrt{441525} \\a = 664.5[/tex]
See how easy it is if you know the theorems.
You could check your results by substituting a and into [tex]a^{2} + c^{2}[/tex] and see if you get get the square of the hypotenuse
