Create two problems that require you to solve using the patterns of both 45-45-90 and 30-60-90 and then solve each problem, show all your work. Include a picture. You will have a problem for a 45-45-90 triangle and a problem for a 30-60-90 triangle.
See the attached image for the drawings of the 45-45-90 triangle and the 30-60-90 triangle.
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For the 45-45-90 triangle, the two legs are both 3 while the hypotenuse is unknown. Call it x for now.
Using trig we can say sin(angle) = opposite/hypotenuse sin(A) = BC/AC sin(45) = 3/x sqrt(2)/2 = 3/x sqrt(2)*x = 2*3 sqrt(2)*x = 6 x = 6/sqrt(2) x = (6/sqrt(2))*(sqrt(2)/sqrt(2)) x = (6*sqrt(2)/(sqrt(2)*sqrt(2)) x = (6*sqrt(2)/(2) x = 3*sqrt(2)
and we can also say sin(angle) = opposite/hypotenuse sin(D) = EF/FD sin(60) = z/y sin(60) = z/8 8*sin(60) = z z = 8*sin(60) z = 8*sqrt(3)/2 z = (8/2)*sqrt(3) z = 4*sqrt(3)
