Verified answer

All angles in a triangle add up to 180 degrees. 75 + 42 = 117; 180 - 117 = 63 degrees; angle S measures 63 degrees.

Use the law of sines to get the lengths of sides r and t. sin(R)/r = sin(S)/s = sin(T)/t

sin(42)/r = sin(63)/5 = sin(75)/t

sin(42)/r = sin(63)/5

sin(42) = r*sin(63)/5

r = [5sin(42)]/sin(63)

sin(63)/5 = sin(75)/t

t*sin(63)/5 = sin(75)

t = [5sin(75)]/sin(63)

Plug those into a calculator to get numbers.

Angle S= 180-75-42=63 degrees

You can use the law of sins to find the other two sides. Sin(T)/t=Sin(S)/s=Sin(R)/r

side r=Sin(42)*5/Sin(63)= 3.8 m

side t=Sin(75)*5/Sin(63)= 5.4 m

∡S = 180°- 75°- 42° = 63°

Use Law of Sines to find sides r and t:

sin 63°/5 = sin 75°/t = sin 42°/r

t = 5sin75°/sin63° ≈ 5.42 m

and

r = 5sin42°/sin63° ≈ 3.755 m