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

What is the length of the altitude from vertex A to side BC in triangle ABC, where AB = 5 cm, AC = 12 cm, and BC = 13 cm? (2023)

What is the length of the altitude from vertex A to side BC in triangle ABC, where AB = 5 cm, AC = 12 cm, and BC = 13 cm? (2023)

Step 1: Identify the sides of triangle ABC. We have AB = 5 cm, AC = 12 cm, and BC = 13 cm.
Step 2: Calculate the semi-perimeter (s) of the triangle using the formula s = (AB + AC + BC) / 2.
Step 3: Substitute the values: s = (5 + 12 + 13) / 2 = 30 / 2 = 15 cm.
Step 4: Use Heron's formula to find the area (A) of the triangle: A = √(s * (s - AB) * (s - AC) * (s - BC)).
Step 5: Substitute the values into Heron's formula: A = √(15 * (15 - 5) * (15 - 12) * (15 - 13)).
Step 6: Calculate the values: A = √(15 * 10 * 3 * 2) = √(900) = 30 cm².
Step 7: Now, use the area to find the altitude from vertex A to side BC using the formula: altitude = (2 * Area) / base.
Step 8: Substitute the area and the length of side BC: altitude = (2 * 30) / 13.
Step 9: Calculate the altitude: altitude = 60 / 13 ≈ 4.62 cm.

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