CHAPTER 8 RIGHT TRIANGLES 8-5 TRIGONOMETRY THE TANGENT RATIO

TRIGONOMETRY Trigonometry is a branch of math that deals with side-angle relationships of triangles. In this and the following sections, we will study right triangle trigonometry.

TRIGONOMETRY When applying trigonometry to right triangles, it is important that we understand the following terms: Hypotenuse Opposite Leg A Adjacent Leg

THE TANGENT RATIO The tangent ratio involves the opposite and adjacent sides of a triangle from a given acute angle. *Tangent of A = leg opposite A / leg adjacent A Hypotenuse Opposite Leg A Adjacent Leg

EXAMPLE Find tan A & tan B. Express answers as ratios. 7 A C 2 B

EXAMPLE Find tan m A and m B A 17 B 8 C

GRADE OF A ROAD The grade of a road is a ratio of its rise to its run and is given as a decimal or percent. The grade of a road is its tangent ratio expressed as a percent. grade Rise (Opp.) Run (Adj.)

EXAMPLE The grade of a road is 7%. What angle does the road make with the horizontal? 4 degrees

PRACTICE Find x to the nearest tenth. 10 10 7 78.2 35° x x 30 21° x

PRACTICE Find y° correct to the nearest degree. 8 58 37 5 y° 8 6 y° 10

CLASSWORK/HOMEWORK 8.5 Assignment Pgs. 306-307, Classroom Exercises 1-11 Pgs. 308-309, Written Exercises 1-20 all