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Apply both trigonometric ratios and Pythagorean Theorem to solve application problems involving right triangles.
Clarifications:

Essential Understandings

Concrete:

  • Label parts of the triangle.
  • Identify the formula for the Pythagorean Theorem.
  • Identify what each variable in the Pythagorean Theorem represents.
  • Given an angle, identify the adjacent sides, opposite sides, and hypotenuse.
  • Given a problem, label a diagram with the given measurements.
Representation:
  • Use a scientific calculator to calculate using the Pythagorean Theorem.
  • Understand the following concepts and vocabulary: Pythagorean Theorem, length, right triangle, adjacent sides, opposite sides, hypotenuse, sine, cosine, tangent, secant, cosecant and cotangent.
  • Use a graphic organizer to find a missing side using the Pythagorean Theorem.
  • Enter information into the formula for the Pythagorean Theorem to solve problems.
  • Use appropriate tools to calculate using the Pythagorean Theorem and trigonometric ratios.
  • Use a scientific calculator to calculate the sine and cosine.
  • Given the trigonometric ratio or relationship, identify the parts of the triangle that relate.
  • Set up the fraction for the trigonometric ratio.

Access Point #: MAFS.912.G-SRT.3.AP.8a (Archived Access Point)
Access Point Standards

Visit the specific benchmark webpage to find related instructional resources.

  • MAFS.912.G-SRT.3.8: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. ★
Access Point Information
Number:
MAFS.912.G-SRT.3.AP.8a
Category:
Access Points
Date Adopted or Revised:
07/14
Cluster:
Define trigonometric ratios and solve problems involving right triangles. (Geometry - Major Cluster) : 

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Access Point Courses
  • Foundational Skills in Mathematics 9-12 (#1200400): This course supports students who need additional instruction in foundational mathematics skills as it relates to core instruction. Instruction will use explicit, systematic, and sequential approaches to mathematics instruction addressing all strands including number sense & operations, algebraic reasoning, functions, geometric reasoning and data analysis & probability. Teachers will use the listed benchmarks that correspond to each students’ needs. 

    Effective instruction matches instruction to the need of the students in the group and provides multiple opportunities to practice the skill and receive feedback. The additional time allotted for this course is in addition to core instruction. The intervention includes materials and strategies designed to supplement core instruction.

  • Precalculus Honors (#1202340): In Precalculus Honors, instructional time will emphasize six areas: (1) extending right triangle trigonometry to unit circle trigonometry and trigonometric functions; (2) extending understanding of functions to trigonometric; (3) developing understanding of conic sections; (4) representing and performing operations with complex numbers and vectors in the coordinate plane; (5) extending understanding of relations in the plane using parametric representations, including polar coordinates and (6) analyzing arithmetic and geometric sequences and series.

    All clarifications stated, whether general or specific to Precalculus Honors, are expectations for instruction of that benchmark.

    Curricular content for all subjects must integrate critical-thinking, problem-solving, and workforce-literacy skills; communication, reading, and writing skills; mathematics skills; collaboration skills; contextual and applied-learning skills; technology-literacy skills; information and media-literacy skills; and civic-engagement skills.

  • Trigonometry Honors (#1211300):
  • Geometry (#1206310): In Geometry, instructional time will emphasize five areas: (1) proving and applying relationships and theorems involving two-dimensional figures using Euclidean geometry and coordinate geometry; (2) establishing congruence and similarity using criteria from Euclidean geometry and using rigid transformations; (3) extending knowledge of geometric measurement to two-dimensional figures and three-dimensional figures; (4) creating and applying equations of circles in the coordinate plane and (5)developing an understanding of right triangle trigonometry.

    All clarifications stated, whether general or specific to Geometry, are expectations for instruction of that benchmark.

    Curricular content for all subjects must integrate critical-thinking, problem-solving, and workforce-literacy skills; communication, reading, and writing skills; mathematics skills; collaboration skills; contextual and applied-learning skills; technology-literacy skills; information and media-literacy skills; and civic-engagement skills.

  • Geometry Honors (#1206320): In Geometry Honors, instructional time will emphasize five areas: (1) proving and applying relationships and theorems involving two-dimensional figures using Euclidean geometry and coordinate geometry; (2) establishing congruence and similarity using criteria from Euclidean geometry and using rigid transformations; (3) extending knowledge of geometric measurement to two-dimensional figures and three-dimensional figures; (4) creating and applying equations of circles in the coordinate plane and (5) developing an understanding of right triangle trigonometry.

    All clarifications stated, whether general or specific to Geometry Honors, are expectations for instruction of that benchmark.

    Curricular content for all subjects must integrate critical-thinking, problem-solving, and workforce-literacy skills; communication, reading, and writing skills; mathematics skills; collaboration skills; contextual and applied-learning skills; technology-literacy skills; information and media-literacy skills; and civic-engagement skills.

  • Geometry for Credit Recovery (#1206315): In Geometry for Credit Recovery, instructional time will emphasize six areas: (1) proving and applying relationships and theorems involving two-dimensional figures using Euclidean geometry and coordinate geometry; (2) establishing congruence and similarity using criteria from Euclidean geometry and using rigid transformations; (3) extending knowledge of geometric measurement to two-dimensional figures and three-dimensional figures; (4) creating and applying equations of circles in the coordinate plane and (5) developing an understanding of right triangle trigonometry.

    All clarifications stated, whether general or specific to Geometry, are expectations for instruction of that benchmark.

    Curricular content for all subjects must integrate critical-thinking, problem-solving, and workforce-literacy skills; communication, reading, and writing skills; mathematics skills; collaboration skills; contextual and applied-learning skills; technology-literacy skills; information and media-literacy skills; and civic-engagement skills.

    Credit Recovery courses are credit bearing courses with specific content requirements defined by state academic standards (SAS). Students enrolled in a Credit Recovery course must have previously attempted the corresponding course (and/or End-of-Course assessment) since the course requirements for the Credit Recovery course are exactly the same as the previously attempted corresponding course. For example, Geometry (1206310) and Geometry for Credit Recovery (1206315) have identical content requirements. It is important to note that Credit Recovery courses are not bound by Section 1003.436(1)(a), Florida Statutes, requiring a minimum of 135 hours of bona fide instruction (120 hours in a school/district implementing block scheduling) in a designed course of study that contains student performance standards, since the students have previously attempted successful completion of the corresponding course. Additionally, Credit Recovery courses should ONLY be used for credit recovery, grade forgiveness, or remediation for students needing to prepare for an End-of-Course assessment retake.

  • Access Geometry (#7912065): Access Courses:

    Access courses are for students with the most significant cognitive disabilities. Access courses are designed to provide students access to grade-level general curriculum. Access points are alternate academic achievement standards included in access courses that target the salient content of Florida’s standards. Access points are intentionally designed to academically challenge students with the most significant cognitive disabilities.