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Trigonometry.notebook March 26, 2014 Trigonometry: Trigonometry is the study of mathematics that deals with the sides and the angles of a right triangle. (Pythagorean Theorem only dealt with the sides of a right triangle.) Using trigonometry, you can find missing sides of a right triangle and you can find missing angles of a right triangle. Just a reminder, 1.) How many degrees are there in a triangle? __________________ 2.) Where is the hypotenuse of a right triangle located? ______________________ 3.) What does the word adjacent mean? ________________________ 4.) What type of letters represent sides of a triangle? ____________________ 5.) What type of letters represent angles (vertices) of a triangle? ________________ There are three different trig formulas that you will be working with. Each formula involves two sides and an angle. The formulas are written out below and the mnemonic students usually memorize is SOH CAH TOA. ...where A is the reference angle. You label the sides of a right triangle based on the reference angle you plan on using in your equation. For example, in right triangle C, label the sides opposite, adjacent, and hypotenuse given the reference angle A. B C A 1 Trigonometry.notebook March 26, 2014 For each triangle below, label all sides and set up an appropriate trig. equation that can find your missing variable. Remember to always refer back to your trig. formulas to setup your equations. 2 Trigonometry.notebook March 26, 2014 3 Trigonometry.notebook March 26, 2014 4 Trigonometry.notebook March 26, 2014 Trigonometry Solving Trig. Equations: Remember your three trig. formulas and the mnemonic SOH CAH TOA: When solving trigonometry equations you need to follow these steps: 1.) Determine what your reference angle A is. 2.) Label your sides opposite, adjacent, and hypotenuse based on that reference angle. 3.) Determine what trig. formula to use. 4.) Solve the remaining equation by getting x alone. a.) If looking for the angle, use the inverse functions (sin1, cos1, and tan1) b.) For all other equations, crossmultiply and get xalone. Always keep the trig. function and the angle together. c.) Round only if they say to, if not, write the full display of your calculator. 5 Trigonometry.notebook March 26, 2014 6 Trigonometry.notebook March 26, 2014 7 Trigonometry.notebook March 26, 2014 8 Trigonometry.notebook March 26, 2014 Try some word problems: Read carefully...the picture is half the battle! 1. A ladder leans against a building. The foot of the ladder is 6 feet from the building. The ladder reaches a height of 14 feet on the building. Find, to the nearest degree, the angle the ladder makes with the ground. 2. In the figure below, ABCD is a rectangle whose perimeter is 30. The length of BE is 12. Find to the nearest degree, the measure of angle E. 3.) Find x and y. 9 Trigonometry.notebook March 26, 2014 10 Trigonometry.notebook March 26, 2014 11 Trigonometry.notebook March 26, 2014 12 Trigonometry.notebook March 26, 2014 13 Trigonometry.notebook March 26, 2014 14 Trigonometry.notebook March 26, 2014 15 Trigonometry.notebook March 26, 2014 16 Trigonometry.notebook March 26, 2014 17 Trigonometry.notebook March 26, 2014 More Trigonometry Practice: Angle of Elevation The angle of elevation is always measured from the ground up. Think of it like an elevator that only goes up. It is always INSIDE the triangle. You can think of the angle of elevation in relation to the movement of your eyes. You are looking straight ahead and you must raise (elevate) your eyes to see the top of something. Angle of Depression The angle of depression is always OUTSIDE the triangle. It is never inside the triangle. You can think of the angle of depression in relation to the movement of your eyes. You are standing at the top of a lighthouse and you are looking straight ahead. You must lower (depress) your eyes to see the boat in the water. Examples: 1. From a point on the ground 25 feet from the foot of a tree, the angle of elevation of the top of the tree is 32º. Find to the nearest foot, the height of the tree. 2.) From the top of a barn 25 feet tall, you see a cat on the ground. The angle of depression of the cat is 40º. How many feet, to the nearest foot, must the cat walk to reach the barn? 18 Trigonometry.notebook March 26, 2014 19 Trigonometry.notebook March 26, 2014 20 Trigonometry.notebook March 26, 2014 21 Trigonometry.notebook March 26, 2014 22 Trigonometry.notebook March 26, 2014 23 Trigonometry.notebook March 26, 2014 24 Trigonometry.notebook March 26, 2014 25 Trigonometry.notebook March 26, 2014 26
