Solving for Angles and Sides in the Ambiguous Case

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Cierra Henderson, MBA |
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Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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| Questions: 20 | Updated: Jan 21, 2026
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1) In △ABC, a = 9, b = 7, A = 40°. Find possible angle B.

Explanation

sinB = (7 sin40°)/9 → B ≈ 30.0° or 150.0°

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About This Quiz
Solving For Angles and Sides In The Ambiguous Case - Quiz

Ready to solve triangles when more than one solution exists? In this quiz, you’ll apply the Law of Sines to find missing angles and sides in ambiguous situations. You’ll calculate both possible angle measures, analyze which triangles can actually exist, and connect the math to real-world geometry problems. By the... see moreend, you’ll have a clear grasp of how to handle dual solutions — and know exactly when and why they occur!
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2) In △ABC, a = 13, b = 15, A = 45°. Find possible angle B.

Explanation

sinB = (15 sin45°)/13 → B ≈ 54.6° or 125.4°

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3) In △ABC, a = 8, b = 10, A = 30°. Find possible angle B.

Explanation

sinB = (10 sin30°)/8 → B ≈ 38.7° or 141.3°

Submit

4) In △ABC, a = 7, b = 5, A = 40°. Find possible angle B.

Explanation

sinB = (5 sin40°)/7 → B ≈ 27.3° or 152.7°

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5) In △ABC, a = 11, b = 13, A = 35°. Find possible angle B.

Explanation

sinB = (13 sin35°)/11 → B ≈ 42.7° or 137.3°

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6) In △ABC, a = 10, b = 11, A = 40°. Find possible angle B.

Explanation

sinB = (11 sin40°)/10 → B ≈ 45.0° or 135.0°

Submit

7) In △ABC, a = 9, b = 11, A = 50°. Find possible angle B.

Explanation

sinB = (11 sin50°)/9 → B ≈ 69.2° or 110.8°

Submit

8) In △ABC, a = 12, b = 9, A = 35°. Find possible angle B.

Explanation

sinB = (9 sin35°)/12 → B ≈ 25.5° or 154.5°

Submit

9) In △ABC, a = 8, b = 9, A = 40°. Find possible angle B.

Explanation

sinB = (9 sin40°)/8 → B ≈ 46.3° or 133.7°

Submit

10) In △ABC, side a = 10, side b = 9, and angle A = 40°. Find possible angle B.

Explanation

sinB = (9 sin40°)/10 → B ≈ 35.4° or 144.6°

Submit

11) In △ABC, a = 8, b = 7, A = 35°. Find possible angle B.

Explanation

sinB = (7 sin35°)/8 → B ≈ 30.1° or 149.9°

Submit

12) In △ABC, a = 12, b = 10, A = 50°. Find possible angle B.

Explanation

sinB = (10 sin50°)/12 → B ≈ 39.6° or 140.4°

Submit

13) In △ABC, a = 7, b = 9, A = 40°. Find possible angle B.

Explanation

sinB = (9 sin40°)/7 → B ≈ 55.8° or 124.2°

Submit

14) In △ABC, a = 9, b = 11, A = 30°. Find possible angle B.

Explanation

sinB = (11 sin30°)/9 → B ≈ 37.7° or 142.3°

Submit

15) In △ABC, a = 15, b = 13, A = 45°. Find possible angle B.

Explanation

sinB = (13 sin45°)/15 → B ≈ 37.8° or 142.2°

Submit

16) In △ABC, a = 6, b = 8, A = 40°. Find possible angle B.

Explanation

sinB = (8 sin40°)/6 → B ≈ 59.0° or 121.0°

Submit

17) In △ABC, a = 10, b = 8, A = 35°. Find possible angle B.

Explanation

sinB = (8 sin35°)/10 → B ≈ 27.3° or 152.7°

Submit

18) In △ABC, a = 11, b = 14, A = 40°. Find possible angle B.

Explanation

sinB = (14 sin40°)/11 → B ≈ 54.9° or 125.1°

Submit

19) In △ABC, a = 7, b = 6, A = 35°. Find possible angle B.

Explanation

sinB = (6 sin35°)/7 → B ≈ 29.5° or 150.5°

Submit

20) In △ABC, a = 14, b = 12, A = 50°. Find possible angle B.

Explanation

sinB = (12 sin50°)/14 → B ≈ 41.0° or 139.0°

Submit
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Cierra Henderson |MBA |
K-12 Expert
Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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In △ABC, a = 9, b = 7, A = 40°. Find possible angle B.
In △ABC, a = 13, b = 15, A = 45°. Find possible angle B.
In △ABC, a = 8, b = 10, A = 30°. Find possible angle B.
In △ABC, a = 7, b = 5, A = 40°. Find possible angle B.
In △ABC, a = 11, b = 13, A = 35°. Find possible angle B.
In △ABC, a = 10, b = 11, A = 40°. Find possible angle B.
In △ABC, a = 9, b = 11, A = 50°. Find possible angle B.
In △ABC, a = 12, b = 9, A = 35°. Find possible angle B.
In △ABC, a = 8, b = 9, A = 40°. Find possible angle B.
In △ABC, side a = 10, side b = 9, and angle A = 40°. Find possible...
In △ABC, a = 8, b = 7, A = 35°. Find possible angle B.
In △ABC, a = 12, b = 10, A = 50°. Find possible angle B.
In △ABC, a = 7, b = 9, A = 40°. Find possible angle B.
In △ABC, a = 9, b = 11, A = 30°. Find possible angle B.
In △ABC, a = 15, b = 13, A = 45°. Find possible angle B.
In △ABC, a = 6, b = 8, A = 40°. Find possible angle B.
In △ABC, a = 10, b = 8, A = 35°. Find possible angle B.
In △ABC, a = 11, b = 14, A = 40°. Find possible angle B.
In △ABC, a = 7, b = 6, A = 35°. Find possible angle B.
In △ABC, a = 14, b = 12, A = 50°. Find possible angle B.
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