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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 • 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 • 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 • 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 • Use the trigonometric functions in your calculator to solve for the angle q 64.4 q 32.2 90o cos(q) = 32.2/64.4 = 0.500; q = 60° Angle Examples • 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 • 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 • Use the trigonometric functions in your calculator to solve for the sides x and y 17.0 y 40o x= 17.0*cos40o =13.0 x y=17.0*sin40o=10.9 Trigonometry • The concepts that we discussed in this lesson will be important when we work with vectors.