SOLUTION: The hypotenuse of a right triangle is 42 cm and its shortest leg is 21 cm. Determine the measure of the other leg and its acute angles ..

Algebra ->  Triangles -> SOLUTION: The hypotenuse of a right triangle is 42 cm and its shortest leg is 21 cm. Determine the measure of the other leg and its acute angles ..      Log On


   

Question 880399: The hypotenuse of a right triangle is 42 cm and its shortest leg is 21 cm. Determine the measure of the other leg and its acute angles ..
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
sin%28A%29=21%2F42=1%2F2 ---> highlight%28A=30%5Eo%29 ---> B=90%5Eo-30%5Eo ---> highlight%28B=60%5Eo%29
system%28A=30%5Eo%2Ccos%28A%29=b%2F42%2Ccos%2830%5Eo%29=sqrt%283%29%2F2%29 ---> b%2F42=sqrt%283%29%2F2 ---> b=42sqrt%283%29%2F2 ---> highlight%28b=21sqrt%283%29%29 or b%5E2%2B21%5E2=42%5E2-->b%5E2%2B441=1764-->b%5E2=1764-441-->b%5E2=1323-->b%5E2=441%2A3-->b=sqrt%28441%2A3%29=sqrt%28441%29%2Asqrt%283%29=highlight%2821sqrt%283%29%29
The approximate value is highlight%28b=36.373%29
So, the acute angles measure highlight%2830%5Eo%29 and highlight%2860%5Eo%29 and the longest leg measures approximately highlight%2836.373cm%29 .