Education Standards
OSPI Statistics and Geometry Instructional Task: Roof Design
Overview
This resource was created by the Washington Office of Superintendent of Public Instruction.
Task
OSPI Statistics and Geometry Instructional Task C
Statistics and Geometry; Standards G-SRT.7, Claim 1; G-SRT.8, Claim 1
Roof Design
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Tim is designing a roof truss in the shape of an isosceles triangle. The design shows the base angles of the truss to have measures of . The horizontal base of the roof truss is across.
Let be the distance along one of the two sloped surfaces of the roof.
- Find using the sine and cosine ratios. Show work.
- Explain why it is possible to find , the same length, using two different trigonometric ratios.
- What is the height of the truss? Show work.
Rubric
Rubric
Question Number | Standard/Claim | Description |
C | G-SRT.7/Claim 1 G-SRT.8/Claim 1
| A 3-point response demonstrates full and complete understanding of the standards and claims by doing all the following:
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A 2-point response demonstrates reasonable understanding of the standards and claims by doing two of the following:
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A 1-point response demonstrates partial understanding of the standards and claims by doing one of the following:
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A 0-point response demonstrates almost no understanding of the standards and claims. |
OSPI Statistics and Geometry Instructional Task C Exemplar
OSPI Statistics and Geometry Instructional Task C
Statistics and Geometry; Standards G-SRT.7, Claim 1; G-SRT.8, Claim 1
Roof Design
|
Tim is designing a roof truss in the shape of an isosceles triangle. The design shows the base angles of the truss to have measures of . The horizontal base of the roof truss is across.
Let be the distance along one of the two sloped surfaces of the roof.
- Find using the sine and cosine ratios. Show work.
- Explain why it is possible to find , the same length, using two different trigonometric ratios.
- What is the height of the truss? Show work.
The angle formed by the peak of the truss and the segment that represents the height of the truss is.
The sloped surface is about 19 feet.
feet |