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 apply the Sine Rule to find a missing side?

Back

To find a missing side using the Sine Rule, rearrange the formula to isolate the side you need. For example, to find side a: a = (b * sin(A)) / sin(B).

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 angle A = 30° and side a = 10, what is the value of side b if angle B = 60°?

Back

Using the Sine Rule: b = (a * sin(B)) / sin(A) = (10 * sin(60°)) / sin(30°) = 17.32.

Front

What is the significance of the Sine Rule in solving triangles?

Back

The Sine Rule is significant because it allows for the calculation of unknown sides or angles in non-right triangles, making it essential for various applications in geometry.

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

How can the Sine Rule be used in real-life applications?

Back

The Sine Rule can be used in fields such as architecture, engineering, and navigation to determine distances and angles.

Front

What is the first step in using the Sine Rule?

Back

Identify the known sides and angles in the triangle and determine which side or angle you need to find.

Front

If side a = 12 and angle A = 45°, what is the value of side c if angle C = 90°?

Back

Using the Sine Rule: c = (a * sin(C)) / sin(A) = (12 * sin(90°)) / sin(45°) = 16.97.

Front

What is the relationship between the sine of an angle and the sides of a triangle?

Back

The sine of an angle in a triangle is the ratio of the length of the opposite side to the length of the hypotenuse.