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
6 boxes of spaghettis for 20 persons so that means 12 boxes for 40 persons since there are 50 persons we have 10 persons left since 10 is equals to 20 divided by 2, divide 6 by 2 which is equals to 3 then add 12 Answer: 15
