Sine Rule

Front

What is the Sine Rule?

Back

The Sine Rule 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).

Front

How do you find a missing side using the Sine Rule?

Back

To find a missing side, rearrange the Sine Rule formula: a = b * (sin(A) / sin(B)), where A and B are the angles opposite to sides a and b respectively.

Front

How do you find a missing angle using the Sine Rule?

Back

To find a missing angle, rearrange the Sine Rule: sin(A) = a * (sin(B) / b), then use the inverse sine function to find angle A.

Front

What is the relationship between angles and sides in a triangle according to the Sine Rule?

Back

The Sine Rule shows that larger angles are opposite longer sides, and smaller angles are opposite shorter sides.

Front

If a triangle has sides a = 6, b = 8, and angle A = 30 degrees, how do you find angle B?

Back

Use the Sine Rule: sin(B) = (b * sin(A)) / a. Calculate B using the inverse sine function.

Front

What is the significance of the Sine Rule in real-world applications?

Back

The Sine Rule is used in various fields such as engineering, architecture, and navigation to solve problems involving triangles.

Front

What is the formula for the Sine Rule?

Back

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

Front

In a triangle, if angle A = 50 degrees and angle B = 60 degrees, how do you find angle C?

Back

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

Front

If side a = 10 cm and angle A = 45 degrees, how do you find side b if angle B = 60 degrees?

Back

Use the Sine Rule: b = a * (sin(B) / sin(A)). Substitute the values to find b.

Front

What is the importance of knowing the Sine Rule for solving triangles?

Back

Knowing the Sine Rule allows you to solve for unknown sides and angles in non-right triangles, expanding your problem-solving capabilities.