3 Objectives Find trigonometric ratios using right triangles. Solve problems using trigonometric ratios.
4 Benchmarks1b. Given exact irrational solutions, determine the best rational estimation. (DOK 2) 1c. Solve real-world or application problems that involve square roots and the Pythagorean Theorem. (DOK 3) 4b. Solve real-world applications and mathematical problems to find missing measurements in right triangles by applying special right triangle relationships, geometric means, or trigonometric functions. (DOK 2) 4e. Apply the relationships of sine, cosine, and tangent to problems involving right triangles. (DOK 2)
5 TrigonometryA branch of mathematics developed for use by astronomers and surveyors.Used to calculate distance or measurementsComes from two Greek termsTrigon: triangleMetron: measure
6 Trigonometric RatiosRatio of the lengths of the sides of a right triangleThree most common ratiosSineCosineTangentThese three ratiosare the“SIN”, “COS”, and “TAN”that you seeon your calculators!
7 Identify the Sides of a Triangle Notice the symbol used torepresent the angle!
8 ThetaThe greek letter Theta is used in geometry to represent an angle.
9 Identify the Sides of a Triangle Which side is thehypotenuse of this triangle?
10 Identify the Sides of a Triangle Which side of the triangle is the side adjacent (or beside) the angle?
11 Identify the Sides of a Triangle Which side of the triangle is theside opposite the angle?
12 You must be able to identify the hypotenuse of the triangle and the sides opposite andadjacent to a particularangle to do well inTrigonometry!
13 Check Your Understanding p. 460 For each angle (angles A and B), identify the hypotenuse, adjacent side, and opposite side.Angle AHypotenuse:Adjacent Side:Opposite Side:ABACBCAngle BHypotenuse:Adjacent Side:Opposite Side:ABBCAC