Final answer:
The length of segment BC in triangle ABC is calculated using the midpoint and the Pythagorean theorem, resulting in an approximate length of 18.36 units.
Step-by-step explanation:
To calculate the length of segment BC in triangle ABC, we need to use the properties of triangles and the given information.
Since M is the midpoint of AC, segment AM is equal to segment MC, which are both half of AC. Given that AC is 18, AM and MC are each 9 units long.
Since M is also the midpoint of BC, and MN is a segment perpendicular to BC with a length of 2 units, triangle MNB is a right-angled triangle (with NB being the hypotenuse and MN being the height).
Using the Pythagorean theorem (a² + b² = c²), we can solve for NB:
- Let NB = x
- MN² + NM² (which is AB² because AB = NM) = x²
- 2² + 9² = x²
- 4 + 81 = x²
- 85 = x²
- x = √85
- NB = √85 <=> BC = 2 x NB (since M is the midpoint of BC)
- BC = 2 x √85
- BC ≈ 18.36 units
Therefore, the length of BC is approximately 18.36 units.