ATURAN COSINUS

Summary

This video tutorial provides a comprehensive guide to the Law of Cosines, a crucial concept in solving triangles. Aimed at high school students, it walks viewers through the formulas used to calculate the lengths of sides and the sizes of angles in any triangle. Through step-by-step examples, the video demonstrates how to apply the law effectively. The presenter also offers simple memory tips to help students recall the formulas. The tutorial includes practical problems and explanations to ensure viewers gain a solid understanding of the Law of Cosines and its applications in trigonometry.

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Q & A

What is the Law of Cosines?

The Law of Cosines is a formula used to relate the sides and angles of a triangle. It is particularly useful in solving non-right-angled triangles when you know two sides and the included angle, or when you have all three sides and need to find an angle.

What is the formula for the Law of Cosines?

The formula for the Law of Cosines is: c² = a² + b² - 2ab * cos(C), where a, b, and c are the lengths of the sides of the triangle, and C is the included angle opposite side c.

How can you remember the Law of Cosines easily?

To remember the Law of Cosines, focus on the three variables: a, b, and c. If you are solving for a particular side, the formula will involve the other two sides and the cosine of the corresponding angle.

What does each part of the Law of Cosines formula represent?

In the Law of Cosines formula, 'a', 'b', and 'c' are the lengths of the sides of the triangle, and 'C' is the angle opposite side 'c'. The formula calculates the length of one side of a triangle when you know the other two sides and the included angle.

How can the Law of Cosines be used to find the length of side 'c'?

To find the length of side 'c', you use the formula: c² = a² + b² - 2ab * cos(C), where 'a' and 'b' are the other two sides, and 'C' is the included angle. You solve for 'c' by rearranging the formula and taking the square root after performing the calculations.

What is the result when using the Law of Cosines for side 'c' with values a=15 cm, b=24 cm, and C=60°?

By applying the Law of Cosines: c² = 15² + 24² - 2 * 15 * 24 * cos(60°), the result is c² = 441, so c = 21 cm.

How do you apply the Law of Cosines to find an angle?

To find an angle, use the formula: cos(A) = (b² + c² - a²) / (2bc), where 'a', 'b', and 'c' are the sides of the triangle, and 'A' is the angle opposite side 'a'. Solve for cos(A) and then use the inverse cosine function (cos⁻¹) to find the angle.

What steps should be followed to find angle A given the sides a=10 cm, b=20 cm, and c=28 cm?

To find angle A, use the formula: cos(A) = (b² + c² - a²) / (2bc). Substituting the values: cos(A) = (20² + 28² - 10²) / (2 * 20 * 28) = 0.967. Thus, angle A = cos⁻¹(0.967) ≈ 14.5°.

What is the significance of using the inverse cosine (cos⁻¹) in the Law of Cosines?

The inverse cosine function (cos⁻¹) is used to determine the angle when the cosine of the angle has been calculated using the Law of Cosines. It converts the cosine value back to the actual angle in degrees.

Can you use any form of the Law of Cosines to solve for a triangle's sides and angles?

Yes, regardless of the form of the Law of Cosines you use, as long as you correctly apply the formula for sides or angles, the final result will always be the same. Different forms simply provide easier solutions depending on what is given in the problem.