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BetterGrades Precalculus · Unit 12 · Unit map

Triangle Trigonometry and Vectors

A ramp rises 0.84 meter over a horizontal run of 7.2 meters. Find its angle of inclination and length.

Precalculus · Unit 12

The lesson path

A ramp rises 0.84 meter over a horizontal run of 7.2 meters. Find its angle of inclination and length.

Core sequence

Triangle Trigonometry and Vectors

Move in order when the material is new, or enter at the exact skill you need.

  1. 01Right triangles and trigonometric ratiosConnect unit-circle trig definitions with ratios in similar right triangles.
  2. 02Right-triangle applicationsModel heights, distances, slopes, and angles of elevation or depression.
  3. 03The Law of SinesDerive and apply the Law of Sines to ASA, AAS, and suitable SSA triangles.
  4. 04The ambiguous SSA caseDetermine whether SSA data produce zero, one, or two triangles.
  5. 05The Law of CosinesUse the Law of Cosines for SAS and SSS data and connect it to the Pythagorean theorem.
  6. 06Triangle area formulasUse K=(12)abK=(\frac{1}{2})ab sin C and compare with base-height and Heron forms.
  7. 07Bearings and navigationTranslate among standard angles, quadrant bearings, headings, and triangle or component models.
  8. 08Vectors geometrically and in componentsRepresent vectors by magnitude and direction, add them geometrically, and convert to components.
  9. 09Vector operations, magnitude, direction, and unit vectorsUse scalar multiplication, normalization, and component resolution.
  10. 10Dot product, angles, and projectionUse the dot product to find angles, test orthogonality, and calculate projections.
Source record

References used for this unit

  • Sundstrom & Schlicker, Trigonometry, Chapter 3
  • Lippman & Rasmussen, Precalculus Vol. 2, 5.5, 8.1, 8.4, 8.5
  • Yoshiwara, Trigonometry, Chapters 2, 3, and 9
  • Corral, Trigonometry, Chapters 1 and 2

The learner copy is original BetterGrades material informed by these rights-separated references; no long source passage is reproduced.