9514 1404 393
Answer:
9) 39.7°
10) insufficient information
11) 20.0 in
12) 19.0 m
Explanation:
These Law of Sines problems are all worked the same way. For sides a, b, and opposite angles A, B, the relevant relationship is ...
a/sin(A) = b/sin(B)
This gives rise to formulas for angle and side:
A = arcsin(a/b·sin(B))
a = b·sin(A)/sin(B)
If the longest given side is not opposite the largest given angle, there may be two solutions.
_____
9) B = arcsin(8/12.5·sin(87°)) = 39.7°
10) missing a side or angle; insufficient information
11) f = (5 in)·sin(70.4°)/sin(13.6°) = 20.0 in
12) p = (22 m)·sin(59°)/sin(180°-59°-24°) = 19.0 m