Answer:
12.68°
Step-by-step explanation:
We know all three sides (18, 80, 82), but we only need two: 18, and 82. Why? What we do here is find the arcsin of the first leg divided by the hypotenuse.
arcsin(18/82)
18/82 is the same as 9/41, which equals 0.21951 repeating (all 5 digits after the decimal are repeating, by the way).
arcsin(0.21951)
What you see above this statement equals 0.22131 radians.
0.22131 rad
To convert this to degrees, multiply by 57.2957795.
0.22131 * 57.2957795
0.22131 times 57.2957795 is 12.680128961145.
12.680128961145°
The directions say the final answer has to be two decimal places. So this becomes 12.68 (0 is less than 5, so round down).
12.68°
Angle A is 12.68°.
