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 a = 6, b = 8, and c = 10?

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

Step 1: Identify the sides of the triangle. We have side a = 6, side b = 8, and side c = 10.
Step 2: Calculate the semi-perimeter (s) of the triangle using the formula s = (a + b + c) / 2.
Step 3: Substitute the values: s = (6 + 8 + 10) / 2 = 12.
Step 4: Use Heron's formula to find the area (A) of the triangle: A = √(s * (s - a) * (s - b) * (s - c)).
Step 5: Substitute the values into Heron's formula: A = √(12 * (12 - 6) * (12 - 8) * (12 - 10)).
Step 6: Calculate the area: A = √(12 * 6 * 4 * 2) = √576 = 24.
Step 7: Use the area to find the altitude (height) from vertex A to side BC. The formula is Area = 1/2 * base * height.
Step 8: Here, the base (BC) is side a = 6. So, we have 24 = 1/2 * 6 * height.
Step 9: Solve for height: 24 = 3 * height, so height = 24 / 3 = 8.

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