In triangle ABC, if AB = 8 cm, AC = 6 cm, and angle A = 60 degrees, what is the

₹0.0

Question: In triangle ABC, if AB = 8 cm, AC = 6 cm, and angle A = 60 degrees, what is the length of side BC using the Law of Cosines?

Options:

Correct Answer: 10 cm

Solution:

Using the Law of Cosines: BC^2 = AB^2 + AC^2 - 2 * AB * AC * cos(A) = 8^2 + 6^2 - 2 * 8 * 6 * (1/2) = 64 + 36 - 48 = 52. Therefore, BC = √52 = 10 cm.

In triangle ABC, if AB = 8 cm, AC = 6 cm, and angle A = 60 degrees, what is the length of side BC using the Law of Cosines?

In triangle ABC, if AB = 8 cm, AC = 6 cm, and angle A = 60 degrees, what is the length of side BC using the Law of Cosines?

Step 1: Identify the sides and angle of triangle ABC. We have AB = 8 cm, AC = 6 cm, and angle A = 60 degrees.
Step 2: Write down the Law of Cosines formula: BC^2 = AB^2 + AC^2 - 2 * AB * AC * cos(A).
Step 3: Substitute the values into the formula: BC^2 = 8^2 + 6^2 - 2 * 8 * 6 * cos(60 degrees).
Step 4: Calculate AB^2: 8^2 = 64.
Step 5: Calculate AC^2: 6^2 = 36.
Step 6: Calculate cos(60 degrees): cos(60 degrees) = 1/2.
Step 7: Substitute the values into the equation: BC^2 = 64 + 36 - 2 * 8 * 6 * (1/2).
Step 8: Calculate 2 * 8 * 6 * (1/2): This equals 48.
Step 9: Now, substitute this back into the equation: BC^2 = 64 + 36 - 48.
Step 10: Add 64 and 36: 64 + 36 = 100.
Step 11: Subtract 48 from 100: 100 - 48 = 52.
Step 12: Take the square root of 52 to find BC: BC = √52.
Step 13: Simplify √52: BC = 10 cm.

Law of Cosines – A formula used to find the length of a side in a triangle when two sides and the included angle are known.
Triangle Properties – Understanding the relationships between the sides and angles of a triangle.