What is the length of the altitude from vertex A to side BC in triangle ABC with

What is the length of the altitude from vertex A to side BC in triangle ABC with sides AB = 6, AC = 8, and BC = 10?

What is the length of the altitude from vertex A to side BC in triangle ABC with sides AB = 6, AC = 8, and BC = 10?

Correct Answer: 4.8

Step 1: Identify the sides of triangle ABC. We have AB = 6, AC = 8, and BC = 10.
Step 2: Calculate the semi-perimeter (s) of the triangle using the formula s = (AB + AC + BC) / 2. So, s = (6 + 8 + 10) / 2 = 12.
Step 3: Use Heron's formula to find the area of the triangle. The formula is Area = sqrt(s * (s - AB) * (s - AC) * (s - BC)).
Step 4: Substitute the values into Heron's formula: Area = sqrt(12 * (12 - 6) * (12 - 8) * (12 - 10)) = sqrt(12 * 6 * 4 * 2).
Step 5: Calculate the area: Area = sqrt(576) = 24.
Step 6: Use the area to find the height (altitude) from vertex A to side BC. The formula is Area = 1/2 * base * height, where base = BC = 10.
Step 7: Rearrange the formula to find height: height = (2 * Area) / base = (2 * 24) / 10.
Step 8: Calculate the height: height = 48 / 10 = 4.8.

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