Law of Sines Challenge

Froggy Jumps

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Sine rule quiz

Created by

Maria Fe Jasareno

Philippines

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1	Maria Fe Jasareno June 10, 2026	% 30	00:23

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Froggy Jumps Law of Sines ChallengeOnline version Sine rule quiz by Maria Fe Jasareno 1 What is the Law of Sines formula for a triangle? a sin A = a, sin B = b, sin C = c b sin A / a = sin B / b = sin C / c c a / sin A = b / sin B = c / sin C 2 In a triangle, if a=7, b=9, and A=40°, what is B (use law of sines)? a ≈55.9° b ≈74.1° c ≈29.7° 3 Given a=5, b=7, A=30°, find C using the law of sines after finding B. a C ≈135.0° b C ≈105.6° c C ≈74.4° 4 Two possible solutions (ambiguous case) arise when which condition holds? a a > b b A > 90° c sin B = (b sin A)/a with 0< (b sin A)/a < 1 5 If a=4, b=5, A=30°, can there be two B values? (ambiguous case) a Yes, B ≈38.7° or 141.3° b Only B≈90° c No, only one value 6 When using the law of sines, what must be true to compute an unknown angle from a known side? a Need at least one angle and the opposite side b Need all three sides c Only sides are enough 7 Given a triangle with a=6, b=8, and A=45°, what is sin B? a sin B = sin A / (b/a) b sin B = a/b c sin B = (b sin A)/a = 8*(√2/2)/6 ≈ 0.9428 8 If sin B ≈ 0.5 and B is acute, what is B? a B = 60° b B = 30° c B = 45° 9 Law of Sines can help find which triangle element when two sides and a non-included angle are known? a An angle opposite a known side b The triangle’s area c The radius 10 Which ratio is constant in the Law of Sines for triangle ABC? a a / sin A = b / sin B = c / sin C b cos A / a = cos B / b = cos C / c c sin A / a = sin B / b = sin C / c

Froggy Jumps

Law of Sines ChallengeOnline version

Sine rule quiz

by Maria Fe Jasareno

What is the Law of Sines formula for a triangle?

sin A = a, sin B = b, sin C = c

sin A / a = sin B / b = sin C / c

a / sin A = b / sin B = c / sin C

In a triangle, if a=7, b=9, and A=40°, what is B (use law of sines)?

≈55.9°

≈74.1°

≈29.7°

Given a=5, b=7, A=30°, find C using the law of sines after finding B.

C ≈135.0°

C ≈105.6°

C ≈74.4°

Two possible solutions (ambiguous case) arise when which condition holds?

a > b

A > 90°

sin B = (b sin A)/a with 0< (b sin A)/a < 1

If a=4, b=5, A=30°, can there be two B values? (ambiguous case)

Yes, B ≈38.7° or 141.3°

Only B≈90°

No, only one value

When using the law of sines, what must be true to compute an unknown angle from a known side?

Need at least one angle and the opposite side

Need all three sides

Only sides are enough

Given a triangle with a=6, b=8, and A=45°, what is sin B?

sin B = sin A / (b/a)

sin B = a/b

sin B = (b sin A)/a = 8*(√2/2)/6 ≈ 0.9428

If sin B ≈ 0.5 and B is acute, what is B?

B = 60°

B = 30°

B = 45°

Law of Sines can help find which triangle element when two sides and a non-included angle are known?

An angle opposite a known side

The triangle’s area

The radius

Which ratio is constant in the Law of Sines for triangle ABC?

a / sin A = b / sin B = c / sin C

cos A / a = cos B / b = cos C / c

sin A / a = sin B / b = sin C / c

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Law of Sines Challenge

Froggy Jumps

About this activity

Created by

Download the paper version to play

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Law of Sines ChallengeOnline version

by Maria Fe Jasareno

What is the Law of Sines formula for a triangle?

In a triangle, if a=7, b=9, and A=40°, what is B (use law of sines)?

Given a=5, b=7, A=30°, find C using the law of sines after finding B.

Two possible solutions (ambiguous case) arise when which condition holds?

If a=4, b=5, A=30°, can there be two B values? (ambiguous case)

When using the law of sines, what must be true to compute an unknown angle from a known side?

Given a triangle with a=6, b=8, and A=45°, what is sin B?

If sin B ≈ 0.5 and B is acute, what is B?

Law of Sines can help find which triangle element when two sides and a non-included angle are known?

Which ratio is constant in the Law of Sines for triangle ABC?

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