Standard #: MA.912.G.5.4 (Archived Standard)


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Solve real-world problems involving right triangles.


Remarks


Example: The distance of the base of a ladder from the wall it leans against should be at least 1/3 of the ladder's total length.  Suppose a 12-ft ladder is placed according to these guidelines.  Give the minimum distance of the base of the ladder from the wall.  How far up the wall will the ladder reach?  Explain and include a sketch in your explanation.

General Information

Subject Area: X-Mathematics (former standards - 2008)
Grade: 912
Body of Knowledge: Geometry
Standard: Right Triangles - Apply the Pythagorean Theorem to solving problems, including those involving the altitudes of right triangles and triangles with special angle relationships. Use special right triangles to solve problems using the properties of triangles.
Date Adopted or Revised: 09/07
Content Complexity Rating: Level 3: Strategic Thinking & Complex Reasoning - More Information
Date of Last Rating: 06/07
Status: State Board Approved - Archived
Assessed: Yes

Test Item Specifications

    Item Type(s): This benchmark may be assessed using: MC , FR item(s)
    Also Assesses:

    MA.912.G.5.1 Prove and apply the Pythagorean Theorem and its converse.

    MA.912.G.5.2 State and apply the relationships that exist when the altitude is drawn to the hypotenuse of a right triangle.

    MA.912.G.5.3 Use special right triangles (30° - 60° - 90° and 45° - 45° - 90°) to solve problems.

    Clarification :
    Students will apply properties of right triangles to solve real-world problems.
    Content Limits :

    Items may require students to apply the Pythagorean theorem, special right triangle relationships, and/or characteristics of triangles resulting from the altitude of a right triangle drawn from the right angle to the hypotenuse.

    Items may include the application of the geometric mean.

    Stimulus Attributes :

    Items assessing MA.912.G.5.2 may be set in either mathematical or real-world contexts. All other items must be set in real-world context.

    Any radical expressions in the item stem must be in simplified or rationalized form.

    Graphics should be used in most of these items, as appropriate.

    Response Attributes :
    Any radical expressions in multiple-choice options will be provided in simplified or rationalized form.


Sample Test Items (2)

Test Item # Question Difficulty Type
Sample Item 1 N/A MC: Multiple Choice
Sample Item 2

Nara created two right triangles. She started with LJKL and drew an altitude from point K to side JL. The diagram below shows LJKL and some of its measurements, in centimeters (cm).

 

Based on the information in the diagram, what is the measure of x to the nearest tenth of a centimeter?

 N/A FR: Fill-in Response


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