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Sine Law Ambiguous Case Worksheet

Explore the ambiguous case of the Sine Law with various triangle scenarios and problem-solving exercises for Grade 10 students.

Grade 10 Math TrigonometrySine Law Ambiguous Case
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Includes

3 Short AnswerMultiple ChoiceFill in the BlanksTrue / False

Standards

CCSS.MATH.CONTENT.HSG.SRT.D.10CCSS.MATH.CONTENT.HSG.SRT.D.11

Topics

Sine LawTrigonometryAmbiguous CaseGrade 10 Math
8 sections · Free to use · Printable
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Sine Law Ambiguous Case

Name:

Date:

Score:

Read each question carefully and show all your work. Round your answers to one decimal place where necessary.

1. In your own words, explain what the 'ambiguous case' of the Sine Law refers to and when it occurs.

2. For triangle ABC, if side a = 10 cm, side b = 15 cm, and angle A = 30°, how many possible triangles can be formed?

a

Zero triangles

b

One triangle

c

Two triangles

d

Cannot be determined

3. The ambiguous case of the Sine Law occurs when you are given two   and a non-included  .

4. For an acute angle A, if a < h (where h is the   from B to AC), then   triangles can be formed.

5. Consider a triangle ABC where a = 8 cm, b = 12 cm, and angle A = 35°. Determine the number of possible triangles and find all possible values for angle B if a triangle exists.

a = 8b = 12A = 35°

6. If angle A is obtuse, and side a is greater than side b, then there is always one unique triangle.

T

True

F

False

7. A surveyor measures two sides of a triangular plot of land to be 75 meters and 100 meters. The angle opposite the 75-meter side is 40°. Find all possible lengths for the third side of the plot.