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Lesson 84 Trigonometry with answers.notebook February 18, 2015 Questions/Main Ideas Lesson 84 Trigonometry trigonometry from Greek, trigon, meaning triangle, and metron , meaning measure Trigonometric Ratios words: sine A = measure of leg opposite A measure of hypotenuse B sin A = BC AB opposite A sin B = AC AB A C opposite B Questions/Main Ideas words: cosine A = measure of leg adjacent A measure of hypotenuse B cos A = AC AB adjacent to B C cos B = BC AB adjacent to A A 1 Lesson 84 Trigonometry with answers.notebook February 18, 2015 Questions/Main Ideas words: tangent A = measure of leg opposite A measure of leg adjacent A B tan A = BC AC adjacent to B and opposite to A tan B = AC BC A C adjacent to A and opposite B Questions/Main Ideas mnemonic device SOH CAH TOA co ta n s = = o ad h= op p h yp jac ad pos yp po e s o ot ite jac ite ten nt en e sin us e us e nt Example 1 Find sin L, cos L, tan L, sin N, cos N, and tan N. Express each ratio as a fraction and as a decimal. 2 Lesson 84 Trigonometry with answers.notebook February 18, 2015 Questions/Main Ideas Example 2 Use a special right triangle to express the cosine of 60 as a fraction and as a decimal to the nearest hundredth. Example 3 Find each value to the nearest ten thousandth (be sure calculator is in degree mode) a. tan 56 b. cos 89 Questions/Main Ideas Example 4 A fitness trainer sets the incline on a treadmill to 7 degrees. The walking surface is 5 feet long. Approximately how many inches did the trainer raise the end of the treadmill from the floor? 3 Lesson 84 Trigonometry with answers.notebook February 18, 2015 Questions/Main Ideas Find the measure of an angle by using the inverse of sine, cosine, or tangent. 4 Lesson 84 Trigonometry with answers.notebook February 18, 2015 Questions/Main Ideas Example 5 Use a calculator to find the measure of P to the nearest tenth. Questions/Main Ideas solving a right triangle finding all of the missing sides and angles you must know two side lengths or one side length and the measure of one acute angle Example 6 Solve the right triangle. Round side measures to the nearest hundredth and angle measures to the nearest degree. 5 Lesson 84 Trigonometry with answers.notebook February 18, 2015 6