Solving for Angles and Sides in the Ambiguous Case

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| Questions: 20 | Updated: Oct 14, 2025
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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! see less

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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°

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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°

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

Explanation

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

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

Explanation

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

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

Explanation

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

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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°

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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°

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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°

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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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