A certain television is advertised as a 95-inch TV (the diagonal length). If the width of the TV is 77 inches, how tall is the TV? Round to the nearest tenth of an inch.
Let $h$ represent the height of the TV. We can create a right triangle, where the width of the TV is the base and the height of the TV is the height. We know that the hypotenuse, which is the diagonal length, is 95 inches. The width is the base and the height is the height, so we can apply the Pythagorean Theorem: $$77^2+h^2=95^2.$$ Expanding, we have $5929+h^2=9025,$ so $h^2=3096.$ Taking the square root of both sides, we find $h\approx\sqrt{3096}\approx 55.6.$ Rounded to the nearest tenth, the height is $\boxed{55.6}$ inches.
