Question
An acute triangle has two sides measuring 8 cm and 10 cm. What is the best representation of the possible range of values for the third side, s? 2 < s < 18 6 < s < 12.8 s < 2 or s > 18 s < 6 or s > 12.8
Answer
2 < s < 18
- Q: What is the triangle inequality theorem? A: The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
- Q: What is an acute triangle? A: An acute triangle is a triangle where all three angles are less than 90 degrees.
- Q: Based on the triangle inequality theorem, what is the range of values for the third side s? A: Since we know that two sides of the triangle measure 8 cm and 10 cm, we can use the triangle inequality theorem to find the possible range of values for the third side s. That is, 10 - 8 < s < 10 + 8. Simplifying this inequality gives us 2 < s < 18.
- Q: Is this an acute triangle? A: Based on the fact that the two sides measuring 8 cm and 10 cm are larger than the third side s, we know that this is an acute triangle.