Question 1146878
you can use the law of sines to solve this.
law of sines says a/sin(A) = b/sin(B) = c/sin(C)
let your triangle be ABC
A is the 90 degree angle.
B is the 40 degree angle.
C is the 50 degree angle.
a is the side opposite angle (A)
b is the side opposite angle (B) 
c is the side opposite angle (C)
measure of side c is 8.
measure of angle (C) is 50 degrees.
since angle A is 90 degrees, then angle B has to be 180 - 90 - 50 = 40 degrees.
law of sines says a/sin(A) = c/sin(C)
c = 8 and C = 50 and A = 90
formula becomes:
a/sin(90) = 8/sin(50)
solve for a to get:
a = 8 * sin(90) / sin(50) = 10.44325831
likewise, .....
c/sin(C) = b/sin(B)
this becomes:
8/sin(50) = b/sin(40)
solve for b to get:
b = 8 * sin(40) / sin(50) = 6.712797049
this is a right triangle where:
the two legs are c and b, and he hypotenuse is a.
your leg measurements are:
c = 8
b = 6.712797049
the hypotenuse measurement is:
c = 10.44325831
in a right triangle, the sum of the square of each leg is equal to the square of the hypotenuse.
that means that 6.712797049^2 + 8^2 = 10.44325831^2
do the math and you will see that 109.0616442 = 109.0616442, confirming that the lengths of the legs and the hypotenuse are correct.
your solution is:
the other acute angle is 40 degrees.
the length of the other leg is 6.712797049
the length of the hypotenuse is 10.44325831
here's my diagram.


<img src = "http://theo.x10hosting.com/2019/101302.jpg" alt="$$$" >