Sine Law Ambiguous Case Worksheet
Explore the ambiguous case of the Sine Law with various triangle scenarios and problem-solving exercises.
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Sine Law Ambiguous Case
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Read each question carefully and solve for all possible values. Show all your work.
1. In ΔABC, side a = 12 cm, side b = 15 cm, and angle A = 40°. Determine the number of possible triangles and solve for all unknown angles and sides.
Diagram for Problem 1:
2. Given ΔXYZ with side x = 8 cm, side y = 10 cm, and angle X = 60°. Investigate if an ambiguous case exists and find all possible solutions.
Diagram for Problem 2:
3. In ΔPQR, angle P = 30°, side p = 5 cm, and side q = 10 cm. How many distinct triangles can be formed?
Zero triangles
One triangle
Two triangles
Cannot be determined
4. Which condition must be met for the ambiguous case (two triangles) of the Sine Law to exist when given angle A, side a, and side b?
a < b sin A
a = b sin A
b sin A < a < b
a ≥ b
5. When solving for an angle using the Sine Law, if the given angle is acute and the opposite side is than the other given side but than the height, then two possible triangles exist.
6. The height (h) of a triangle, when using the Sine Law ambiguous case with angle A and side b, is calculated as h = .
7. If the given angle in an SSA case is obtuse, there can still be an ambiguous case.
True
False
8. If side 'a' is greater than or equal to side 'b' (a ≥ b) when angle A is acute, then only one triangle exists.
True
False
9. A surveyor is trying to measure the distance across a lake. From point A, the distance to point C is 500 m, and the distance to point B is 350 m. The angle at A is 30°. How many possible lengths are there for the distance BC? Calculate all possible lengths.
Diagram for Problem 9: