Law of Sines

Front

What is the Law of Sines?

Back

The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. It can be expressed as: a/sin(A) = b/sin(B) = c/sin(C).

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CCSS.HSG.SRT.D.11

Front

How do you use the Law of Sines to find an unknown side?

Back

To find an unknown side using the Law of Sines, rearrange the formula to solve for the side: a = b * (sin(A) / sin(B)).

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Front

How do you use the Law of Sines to find an unknown angle?

Back

To find an unknown angle using the Law of Sines, rearrange the formula to solve for the angle: A = sin^(-1)(a * (sin(B) / b)).

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CCSS.HSG.SRT.D.11

Front

What is the relationship between angles and sides in a triangle according to the Law of Sines?

Back

The Law of Sines shows that larger angles are opposite longer sides, and smaller angles are opposite shorter sides.

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CCSS.HSG.SRT.D.11

Front

If a triangle has sides a = 10, b = 15, and angle A = 30 degrees, how can you find angle B?

Back

Use the Law of Sines: sin(B) = (b * sin(A)) / a. Calculate B using the inverse sine function.

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CCSS.HSG.SRT.D.11

Front

What is the significance of the Law of Sines in solving triangles?

Back

The Law of Sines is significant because it allows for the calculation of unknown sides and angles in non-right triangles.

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Front

What type of triangles can the Law of Sines be applied to?

Back

The Law of Sines can be applied to any triangle, including acute, obtuse, and right triangles.

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What is the formula for the Law of Sines?

Back

The formula is: a/sin(A) = b/sin(B) = c/sin(C).

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How can the Law of Sines help in real-world applications?

Back

The Law of Sines can be used in fields such as navigation, architecture, and engineering to solve problems involving triangles.

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CCSS.HSG.SRT.D.11

Front

If angle A = 45 degrees and angle B = 60 degrees in a triangle, how do you find angle C?

Back

Angle C can be found using the triangle sum property: C = 180 - (A + B).

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