Given a right triangle, use the Pythagorean Theorem to find "a" (one of the legs) when c = 85 and b = 53. (Round your answer to the nearest tenth.)
$$c^2=a^2+b^2\\\\ \Rightarrow a^2 = c^2 -b^2 = (c-b)(c+b)=(85-53)(85+53)=32*138\\ =16*2*2*69\\\\ a=\sqrt{16*4*69}=\sqrt{16}\sqrt{4}\sqrt{69}=4*2*\sqrt{69}=8\sqrt{69}\approx66.5$$
The other leg is found by taking the square root of the difference between the hypoteneuse squared and the other leg squared......i.e, ........
√(852 - 532) ≈ 66.5 ......rounded to the nearest tenth....
And that's it!!!
