12-12-24 Law of Cosines

Front

What is the Law of Cosines?

Back

The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles. It is expressed as: c² = a² + b² - 2ab * cos(C), where C is the angle opposite side c.

Front

What is the formula to find the length of a side using the Law of Cosines?

Back

The formula is: c² = a² + b² - 2ab * cos(C), where c is the side opposite angle C, and a and b are the other two sides.

Front

How do you find an angle using the Law of Cosines?

Back

To find an angle, rearrange the Law of Cosines formula: C = cos⁻¹((a² + b² - c²) / (2ab)).

Front

What is the significance of the Law of Cosines in triangle calculations?

Back

It allows for the calculation of unknown side lengths or angles in any triangle, not just right triangles.

Front

What is the relationship between bearings and angles in navigation?

Back

Bearings are measured clockwise from the north direction, while angles in triangles can be measured in any direction.

Front

How do you convert a bearing to an angle?

Back

To convert a bearing to an angle, subtract the bearing from 360° if it is measured clockwise from the north.

Front

What is the formula for the area of a triangle using the Law of Cosines?

Back

Area = 1/2 * a * b * sin(C), where a and b are two sides and C is the included angle.

Front

What is the sine rule in relation to the Law of Cosines?

Back

The sine rule states that a/sin(A) = b/sin(B) = c/sin(C), which can be used alongside the Law of Cosines for solving triangles.

Front

How do you find the distance between two points using the Law of Cosines?

Back

Use the Law of Cosines to calculate the distance by treating the points as vertices of a triangle.

Front

What is the importance of rounding in navigation calculations?

Back

Rounding is important to provide clear and concise answers, especially in navigation where precision is key.