In triangle ABC, if AB = 12 cm, AC = 16 cm, and angle A = 60 degrees, what is th

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Question: In triangle ABC, if AB = 12 cm, AC = 16 cm, and angle A = 60 degrees, what is the length of BC?

Options:

Correct Answer: 14 cm

Solution:

Using the Law of Cosines: BC² = AB² + AC² - 2(AB)(AC)cos(A) = 12² + 16² - 2(12)(16)(0.5) = 144 + 256 - 192 = 208. Therefore, BC = √208 = 14.42 cm.

In triangle ABC, if AB = 12 cm, AC = 16 cm, and angle A = 60 degrees, what is the length of BC?

In triangle ABC, if AB = 12 cm, AC = 16 cm, and angle A = 60 degrees, what is the length of BC?

Step 1: Identify the sides and angle of triangle ABC. We have AB = 12 cm, AC = 16 cm, and angle A = 60 degrees.
Step 2: Recall the Law of Cosines formula: BC² = AB² + AC² - 2(AB)(AC)cos(A).
Step 3: Substitute the values into the formula. Here, AB = 12, AC = 16, and cos(60 degrees) = 0.5.
Step 4: Calculate AB²: 12² = 144.
Step 5: Calculate AC²: 16² = 256.
Step 6: Calculate 2(AB)(AC)cos(A): 2(12)(16)(0.5) = 192.
Step 7: Substitute these values back into the formula: BC² = 144 + 256 - 192.
Step 8: Perform the addition and subtraction: 144 + 256 = 400, then 400 - 192 = 208.
Step 9: Take the square root of 208 to find BC: BC = √208.
Step 10: Calculate the square root: BC ≈ 14.42 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 in a triangle.