Exercises for Question Type 4: Determining if given information on a triangle suffers from Ambigious case of sine rule

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Exercises for Question Type 4: Determining if given information on a triangle suffers from Ambigious case of sine rule - IB

Question 1

Determine whether a triangle A B C exists for sin A = 0.9, a = 15, and b = 20 . Justify your answer.

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Question 2

Determine whether the given data sin A = 0.8, a = 9, and b = 10 yields one triangle, two triangles, or no triangle. Justify your answer.

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Question 3

Given sin A = 0.5, a = 12, and b = 7, find all possible values of angle B .

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Question 4

For sin A = 0.6, a = 8, and b = 7, determine all possible measures of angle B .

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Question 5

The question tests the understanding of the ambiguous case of the sine rule or the conditions for the existence of a triangle given two sides and a non-included angle.

Determine whether a triangle A B C exists given sin A = 0.8, a = 5, and b = 10 . Explain your reasoning.

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Question 6

Using sin A = 0.7, a = 15, and b = 12, and given that angle A is acute, calculate side c for each possible triangle.

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Question 7

The following question tests the application of the Sine Rule in the ambiguous case (SSA) to find multiple possible values for an angle in a triangle.

In triangle A B C, sin A = 0.4, a = 12, and b = 18 . Find both possible values of angle B . Give your answers correct to one decimal place.

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Question 8

Determine whether a triangle A B C is possible given sin A = 0.6, a = 3, and b = 8 . Justify your answer.

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Question 9

Given sin A = 0.7, a = 15, and b = 12, find the possible value(s) of angle B .

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Question 10

Questions involving the sine rule and the ambiguous case of the triangle.

For the data sin A = 0.5, a = 12, and b = 7, calculate the corresponding measures of angle C for both possible triangles.

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Question 11

Determine all possible values of B if sin A = 0.9, a = 20, and b = 19 .

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IB Mathematics Applications & Interpretation Question Type 4: Determining If Given Information on a Triangle Suffers from Ambigious Case of Sine Rule Exercises