1. 60,30,90 right triangle. y will be hypotenuse/2, x will be hypotenuse*sqrt(3)/2. So x = 16*sqrt(3)/2 = 8*sqrt(3), approximately 13.85640646 y = 16/2 = 8 2. 45,45,90 right triangle (2 legs are equal length and you have a right angle). X and Y will be the same length and that will be hypotenuse * sqrt(2)/2. So x = y = 8*sqrt(2) * sqrt(2)/2 = 8*2/2 = 8 3. Just a right triangle with both legs of known length. Use the Pythagorean theorem x = sqrt(12^2 + 5^2) = sqrt(144 + 25) = sqrt(169) = 13 4. Another right triangle with 1 leg and the hypotenuse known. Pythagorean theorem again. y = sqrt(1000^2 - 600^2) = sqrt(1000000 - 360000) = sqrt(640000) = 800 5. A 45,45,90 right triangle. One leg known. The other leg will have the same length as the known leg and the hypotenuse can be discovered with the Pythagorean theorem. x = 6. y = sqrt(6^2 + 6^2) = sqrt(36+36) = sqrt(72) = sqrt(2 * 36) = 6*sqrt(2), approximately 8.485281374 6. Another 45,45,90 triangle with the hypotenuse known. Both unknown legs will have the same length. And Pythagorean theorem will be helpful. x = y. 12^2 = x^2 + y^2 12^2 = x^2 + x^2 12^2 = 2x^2 144 = 2x^2 72 = x^2 sqrt(72) = x 6*sqrt(2) = x x is approximately 8.485281374 7. A 30,60,90 right triangle with the short leg known. The hypotenuse will be twice the length of the short leg and the remaining leg can be determined using the Pythagorean theorem. y = 11*2 = 22. x = sqrt(22^2 - 11^2) = sqrt(484 - 121) = sqrt(363) = sqrt(121 * 3) = 11*sqrt(3). Approximately 19.05255888 8. A 30,60,90 right triangle with long leg known. Can either have fact that in that triangle, the legs have the ratio of 1:sqrt(3):2, or you can use the Pythagorean theorem. In this case, I'll use the 1:2 ratio between the unknown leg and the hypotenuse along with the Pythagorean theorem. x = 2y y^2 = x^2 - (22.5*sqrt(3))^2 y^2 = (2y)^2 - (22.5*sqrt(3))^2 y^2 = 4y^2 - 1518.75 -3y^2 = - 1518.75 y^2 = 506.25 = 2025/4 y = sqrt(2025/4) = sqrt(2025)/sqrt(4) = 45/2 Therefore: y = 22.5 x = 2*y = 2*22.5 = 45 9. Just a generic right triangle with 2 known legs. Use the Pythagorean theorem. x = sqrt(16^2 + 30^2) = sqrt(256 + 900) = sqrt(1156) = 34 10. Another right triangle, another use of the Pythagorean theorem. x = sqrt(50^2 - 14^2) = sqrt(2500 - 196) = sqrt(2304) = 48
