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 or enter at the exact skill you need.
- 01Right triangles and trigonometric ratiosConnect unit-circle trig definitions with ratios in similar right triangles.
- 02Right-triangle applicationsModel heights, distances, slopes, and angles of elevation or depression.
- 03The Law of SinesDerive and apply the Law of Sines to ASA, AAS, and suitable SSA triangles.
- 04The ambiguous SSA caseDetermine whether SSA data produce zero, one, or two triangles.
- 05The Law of CosinesUse the Law of Cosines for SAS and SSS data and connect it to the Pythagorean theorem.
- 06Triangle area formulasUse sin C and compare with base-height and Heron forms.
- 07Bearings and navigationTranslate among standard angles, quadrant bearings, headings, and triangle or component models.
- 08Vectors geometrically and in componentsRepresent vectors by magnitude and direction, add them geometrically, and convert to components.
- 09Vector operations, magnitude, direction, and unit vectorsUse scalar multiplication, normalization, and component resolution.
- 10Dot product, angles, and projectionUse the dot product to find angles, test orthogonality, and calculate projections.
Review, practice, demonstrate, investigate
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