Law of Cosines Practice

Front

What is the Law of Cosines?

Back

The Law of Cosines states that for any triangle with sides a, b, and c, and corresponding angles A, B, and C, the relationship is: c² = a² + b² - 2ab * cos(C).

Front

When do you use the Law of Cosines?

Back

The Law of Cosines is used when you know two sides and the included angle (SAS) or all three sides (SSS) of a triangle.

Front

Find angle Z if a = 10, b = 15, c = 20.

Back

Z = cos⁻¹((a² + b² - c²) / (2ab)) = cos⁻¹((10² + 15² - 20²) / (2 * 10 * 15)) = 71.23°.

Front

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

Back

To find side c: c² = a² + b² - 2ab * cos(C).

Front

If a = 8, b = 6, and angle C = 60°, find side c.

Back

c = √(a² + b² - 2ab * cos(C)) = √(8² + 6² - 2 * 8 * 6 * 0.5) = 4.

Front

What is the relationship between the angles and sides in a triangle according to 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.

Front

Find the missing side QR if Q = 10 km, R = 15 km, and angle P = 60°.

Back

QR = √(Q² + R² - 2QR * cos(P)) = √(10² + 15² - 2 * 10 * 15 * 0.5) = 7.5 km.

Front

What is the cosine of 90 degrees?

Back

The cosine of 90 degrees is 0.

Front

If c = 25, a = 20, and b = 15, find angle C.

Back

C = cos⁻¹((a² + b² - c²) / (2ab)) = cos⁻¹((20² + 15² - 25²) / (2 * 20 * 15)) = 60°.

Front

What is the Law of Sines?

Back

The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant: a/sin(A) = b/sin(B) = c/sin(C).