Answer:
Step-by-step explanation:
The Law of Sines is useful for this. It tells you ...
r/sin(R) = p/sin(P) = q/sin(Q)
First, we can find angle P, then use the sum of angles of a triangle to find angle R. Finally, we can use the ratios again to find the length r.
Solving the equation for P, we get ...
sin(P) = (p/q)sin(Q)
P = arcsin(p/q·sin(Q)) = arcsin(14/14.6·sin(53°)) ≈ 49.98° ≈ 50°
R = 180° -53° -49.98° = 77.02°
Solving the ratios for r gives ...
r = q·sin(R)/sin(Q) = 14.6·sin(77.02°)/sin(53°) ≈ 17.81 ≈ 17.8
The remaining 3 triangle measures are r = 17.8, P = 50°, R = 77°.
