Directions:Use the SOLVE(S- determine information that is needed to solve the problem. O - communicate an accurate, organized solution path that is aligned to the problem L- using appropriate, effective, and essentially precise representations. V-contain minor flaws that do not detract from correct modeling or demonstration of a thorough understanding. E- Evaluate or validate a partial or complete solution and show how to improve or refine the) Method to complete the following problem: The Problem:
The drawing for a right triangular roof truss, represented by ABC, is shown below. The width of the truss is 10 meters and will span from one side of the house to the other. The homeowner doesn't want this truss to be more than 3 meters from its base to its highest point so they can enjoy the sunset.
If the horizontal distance from A to the highest point of the truss, represented in this figure by AD is 2 meters, will this triangular truss satisfy the requirement of the homeowner?
Local ordinance limits the height of houses to 10 meters. If the house has a square lay-out with a side of 8 meters and a wall height of % the side length, will the house satisfy the ordinance?
S: To solve this problem, we need to determine if the height of the triangular roof truss and the house satisfy the given conditions.
O:
1. Calculate the height of the triangular roof truss using the Pythagorean theorem.
2. Determine if the height of the triangular roof truss is less than 3 meters as specified by the homeowner.
3. Calculate the total height of the house based on the square lay-out and wall height information.
4. Compare the total height of the house with the local ordinance limit of 10 meters.
5. Determine if the house satisfies the ordinance.
L:
1. To calculate the height of the triangular roof truss, we can use the Pythagorean theorem: AC^2 = AB^2 + BC^2
AC^2 = 10^2 + 2^2
AC^2 = 100 + 4
AC^2 = 104
AC = √104
AC ≈ 10.20 meters
2. The height of the triangular roof truss is 10.20 meters, which exceeds the homeowner's requirement of not being more than 3 meters.
3. The total height of the house can be calculated as: 10 (wall height) + 8 (side length) = 18 meters
4. The total height of the house is 18 meters, which exceeds the local ordinance limit of 10 meters.
V: The calculations and comparisons are accurate and clear but could be visually represented with a diagram for better understanding.
E: In order for the triangular roof truss to satisfy the homeowner's requirement, it would need to be redesigned to have a maximum height of 3 meters. Similarly, the house would need to be redesigned to comply with the local ordinance limit of 10 meters. This could involve adjusting the proportions and dimensions of both structures.