A diagonal of a TV is 26 inches long. Assuming that this diagonal forms a pair of 30-60-90 right triangles, what are the exact length and width of the TV?

Answer 1

in a 30-60-90 right triangle, the side opposite the 30 degree angle is half of the hypotenuse

assume the 30 degree angle is bottom right

the width, top to bottom, is therefore 13 inches

now use the Pythagorean Theorem to find the length, left to right

13^2+l^2=26^2

169+l^2=676

l^2=676-169

l^2=507

l=22.51666... inches in length

l=22 1705/3300

l=22 155/300

l=22 31/60 inches exactly