Law of Cosine

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 a and b are the lengths of the sides, C is the included angle, and c is the length of the side opposite angle C.

Front

When is the Law of Cosines used?

Back

The Law of Cosines is used to find a side of a triangle when two sides and the included angle are known, or to find an angle when all three sides are known.

Front

Calculate the area of a triangle with sides 6 m, 8 m, and included angle 137° using the Law of Cosines.

Back

Area = 0.5 * a * b * sin(C) = 0.5 * 6 * 8 * sin(137°) ≈ 16.4 m².

Front

What is the formula for the area of a triangle using two sides and the included angle?

Back

Area = 0.5 * a * b * sin(C), where a and b are the lengths of the sides and C is the included angle.

Front

Find the length of side XZ in a triangle with sides 5 cm, 8 cm, and included angle 39° using the Law of Cosines.

Back

XZ = √(5² + 8² - 2 * 5 * 8 * cos(39°)) ≈ 6.5 cm.

Front

What does 'included angle' mean in the context of triangles?

Back

The included angle is the angle formed between two sides of a triangle.

Front

If a triangle has sides of lengths 5 cm and 8 cm with an included angle of 39°, what is the area?

Back

Area = 0.5 * 5 * 8 * sin(39°) ≈ 12.6 cm².

Front

How do you find the length of a side using the Law of Cosines?

Back

Rearrange the Law of Cosines formula: c = √(a² + b² - 2ab * cos(C)).

Front

What is the significance of the cosine function in the Law of Cosines?

Back

The cosine function relates the angle of the triangle to the lengths of the sides, allowing for the calculation of unknown lengths or angles.

Front

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

Back

The Law of Cosines shows that the square of one side is equal to the sum of the squares of the other two sides minus twice the product of those sides and the cosine of the included angle.