In triangle ABC, if the lengths of the sides are a = 8, b = 15, and c = 17, what

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Question: In triangle ABC, if the lengths of the sides are a = 8, b = 15, and c = 17, what is the value of cos A?

Options:

Correct Answer: 0.8

Solution:

Using the cosine rule, cos A = (b² + c² - a²) / (2bc) = (15² + 17² - 8²) / (2 * 15 * 17) = 0.8.

In triangle ABC, if the lengths of the sides are a = 8, b = 15, and c = 17, what is the value of cos A?

In triangle ABC, if the lengths of the sides are a = 8, b = 15, and c = 17, what is the value of cos A?

Correct Answer: 0.8

Step 1: Identify the sides of the triangle. We have side a = 8, side b = 15, and side c = 17.
Step 2: Write down the cosine rule formula: cos A = (b² + c² - a²) / (2bc).
Step 3: Calculate b² (15²) which is 225.
Step 4: Calculate c² (17²) which is 289.
Step 5: Calculate a² (8²) which is 64.
Step 6: Substitute the values into the formula: cos A = (225 + 289 - 64) / (2 * 15 * 17).
Step 7: Calculate the numerator: 225 + 289 = 514, then 514 - 64 = 450.
Step 8: Calculate the denominator: 2 * 15 * 17 = 510.
Step 9: Now divide the numerator by the denominator: cos A = 450 / 510.
Step 10: Simplify the fraction: 450 / 510 = 0.8824 (approximately).
Step 11: Round the answer to two decimal places if needed, but the exact value is 0.8824.

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