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?
Practice Questions
1 question
Q1
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?
4.8
5
6
7.2
Using the area formula, Area = 1/2 * base * height. The area can also be calculated using Heron's formula, which gives 24. Thus, height = (2 * Area) / base = (2 * 24) / 10 = 4.8.
Questions & Step-by-step Solutions
1 item
Q
Q: 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?
Solution: Using the area formula, Area = 1/2 * base * height. The area can also be calculated using Heron's formula, which gives 24. Thus, height = (2 * Area) / base = (2 * 24) / 10 = 4.8.
Steps: 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)).
