Question

Consider the right triangle ABC given below:

A. What is the length of the hypotenuse of triangle ABC?

B. What is the length of the shorter leg of triangle ABC?

C. What is the length of the longer leg of triangle ABC?

Answer 1

Will do it backward - 
the length of the longer leg of triangle ABC = BC
consider one of the small triangles: sin30 = 10/BC
so BC = 10/sin30 = 10/0.5 = 20

the length of the shorter leg of triangle ABC = AC
consider the other small triangles: sin60 = 10/AC
so AC = 10/sin60 = 10/0.866 = 11.55

the length of the hypotenuse of triangle ABC = AB
= sqrt (BC^2 + AC^2) = sqrt (20^2 +11.55^2)
= 23.09

Answer 2

Hey there,

Your answers would be 

20 

11.55

 23.09

Hope this helps.

~Jurgen