Lesson Objectives SWKOL how to use trigonometry to obtain values of sides and angles of right triangles

Trigonometry Trigonometry relates the various sides and angles of right triangles It is important to remember that all triangles have angles totaling 180° Because a right triangle always has an angle of 90°, the other two angles must add up to 90° also

Angle Examples What is the missing angle theta (q)? 56° q 34°

Angle Examples What is the missing angle theta (q)? 72° q 18°

Trigonometry Three functions in trigonometry relate the angles of a right triangle to its sides: sine, cosine, and tangent By knowing how to use these functions, you can determine the value of any side of a right triangle when given the value of one side and angle

Trigonometry There are three anagrams to remember the trigonometric functions SOH: Sin(q) = opposite/hypotenuse CAH: Cos(q) = adjacent/hypotenuse TOA: Tan(q) = opposite/adjacent

Trigonometry The hypotenuse is the side opposite to the right angle The opposite side is the side opposite to the angle theta (q) The adjacent side is the side next to the angle theta (q) that is not the hypotenuse

Sides of a right triangle hypotenuse opposite 90o Θ adjacent

Side Examples sin(60°) = 0.866 = x/15; x = 13 Use the trigonometric functions in your calculator to solve for the side X 60° 15 90o X sin(60°) = 0.866 = x/15; x = 13

Side Examples cos(45°) = 0.7071 = x/7.3; x = 5.2 Use the trigonometric functions in your calculator to solve for the side X 45° 7.3 X 90o cos(45°) = 0.7071 = x/7.3; x = 5.2

Side Examples tan(30°) = 0.5774 = 53.7/x; x = 93.0 Use the trigonometric functions in your calculator to solve for the side X 53.7 90o 30° X tan(30°) = 0.5774 = 53.7/x; x = 93.0

Trigonometry You can also solve for the angles of a right triangle by using the same equations if you are given two of the sides

Angle Examples cos(q) = 32.2/64.4 = 0.500; q = 60° Use the trigonometric functions in your calculator to solve for the angle q q 64.4 32.2 90o cos(q) = 32.2/64.4 = 0.500; q = 60°

Angle Examples tan(q) = 8.7/5.0 = 1.7; q = 60° Use the trigonometric functions in your calculator to solve for the angle q q 5.0 8.7 tan(q) = 8.7/5.0 = 1.7; q = 60°

Angle Examples sin(q) = 12.4/17.5 = 0.709; q = 45° Use the trigonometric functions in your calculator to solve for the angle q 17.5 12.4 q sin(q) = 12.4/17.5 = 0.709; q = 45°

Side Examples x= 17.0*cos40o =13.0 y=17.0*sin40o=10.9 Use the trigonometric functions in your calculator to solve for the sides x and y 17.0 y 40o x x= 17.0*cos40o =13.0 y=17.0*sin40o=10.9

Trigonometry The concepts that we discussed in this lesson will be important when we work with vectors.