What is the length of the missing side UG? Round answer to the nearest tenth. Thanks for help

For a triangle we have (law of sines):

u/sin(U)=f/sin(F)=g/sin(G), where u, f and g are the sides opposed to angles U, F and G.

We need to compute f:

45/sin(41)=f/sin(77).

We find:

f=45×sin(77)/sin(41)=66.83mm.

f=66.8mm (rounded to tenth)

Step-by-step explanation:

Considering the given triangle FGU, to determine angle UG, we would apply the sine rule. It is expressed as

a/SinA = b/SinB = c/SinC

Where a, b and c are the length of each side of the triangle and angle A, Angle B and angle C are the corresponding angles of the triangle. Likening it to the given triangle, the expression becomes

UG/SinF = UF/SinG = GF/SinU

Therefore

UG/Sin 77 = 45/Sin 41

Cross multiplying, it becomes

UGSin41 = 45Sin77

0.6561UG = 45 × 0.9744

0.6561UG = 43.848

UG = 43.848/0.6561

UG = 66.8mm to the nearest tenth

the probability is 0