Step One Find z All triangles have 180 degrees. No exceptions. z + 47 + 90 = 180 combine like terms on the left. z + 137 = 180 subtract 137 from both sides z = 180 - 137 z = 43 degrees.
Step Two Use the sine function to find y Sin(43) = opposite side / hypotenuse opposite side = 35
sin(43) = 35 / hypotenuse hypotenuse = 35 / sin(43) y = 35/0.6820 y = 51.32
Solve using cos(x) Note this problem could have been done in a shorter way. Cos(47) = adjacent / hypotenuse. hypotenuse = adjacent / cos(47) y = 35 / cos(47) y = 35 / 0.6820 y = 51.32 Both answers agree. It is a good thing to know how to do this question both ways.
