Answer:
82°
Step-by-step explanation:
You are given two sides and the angle opposite one of them. This is sufficient information to make use of the Law of Sines to solve the triangle.
The angle (C) opposite the 89 m side can be found from the proportion ...
sin(C)/89 = sin(30°)/48 . . . . . law of sines applied to the given information
Multiplying by 89 and taking the inverse sine, we have ...
C = arcsin(89/48·sin(30°)) ≈ 67.98°
Then the unknown marked angle (E) between the sides is found using the fact that the sum of angles of a triangle is 180°.
30° + E + C = 180°
E = 150° -C ≈ 82.02° . . . . . . subtract 30°+C from both sides, substitute for C
Rounded to the nearest degree, the angle Devora turned was 82°.
_____
We have chosen to use the letter C to represent the angle at the Cave entrance; and the letter E to represent the angle at the Empty treasure chest.
The value we chose for angle C is the acute angle in accordance with the problem statement. There is another solution to the triangle in which this angle is the obtuse angle 112.02° = 180° - 67.98°.
