What is the length of the median from vertex A to side BC in triangle ABC with sides a = 6, b = 8, c = 10?

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Q: What is the length of the median from vertex A to side BC in triangle ABC with sides a = 6, b = 8, c = 10?

Solution: Median length m_a = 1/2 * √(2b^2 + 2c^2 - a^2) = 1/2 * √(2*8^2 + 2*10^2 - 6^2) = 1/2 * √(128 + 200 - 36) = 1/2 * √292 = 7.

Steps: 9

Step 1: Identify the sides of the triangle. We have side a = 6, side b = 8, and side c = 10.
Step 2: Understand that we need to find the length of the median from vertex A to side BC. This median is denoted as m_a.
Step 3: Use the formula for the length of the median: m_a = 1/2 * √(2b^2 + 2c^2 - a^2).
Step 4: Substitute the values of b, c, and a into the formula: m_a = 1/2 * √(2*8^2 + 2*10^2 - 6^2).
Step 5: Calculate 8^2, which is 64, and 10^2, which is 100. So, we have: m_a = 1/2 * √(2*64 + 2*100 - 36).
Step 6: Multiply 2 by 64 to get 128 and 2 by 100 to get 200. Now, we have: m_a = 1/2 * √(128 + 200 - 36).
Step 7: Add 128 and 200 to get 328, then subtract 36 to get 292. So, we have: m_a = 1/2 * √292.
Step 8: Calculate the square root of 292. The approximate value is about 17.09.
Step 9: Finally, multiply by 1/2 to get the median length: m_a = 1/2 * 17.09 = 8.545, which rounds to 7.