MFM2P Trigonometry Checklist 1 Goals for this unit: I can solve problems involving right triangles using the primary trig ratios and the Pythagorean Theorem. U1L4 The Pythagorean Theorem Learning Goal: I can explain and apply the Pythagorean Theorem. U1L5 The Primary Trigonometric Ratios Learning Goal: I can explain when to use the Sine, Cosine and Tangent ratios and use the functions to determine the missing side or angle. U1L6 Solving Problems using Right Triangles Learning Goal: I can determine which primary trig ratio applies to the real - world situation and solve for the appropriate value. Review Note Page 49, #1-13 Journal One Note Page 71, #1 14 Page 79, #1-14 Journal Two Note Page 86, # 1-13 Journal Three Page 88 #6,7,10,11,13,15-17 Page 90
MFM 2P U1L5 Pythagorean Theorem Today's Topic : Pythagorean Relation Today's Goal : I can solve for the missing side in a right triangle by using the Pythagorean relation 2.1 The Pythagorean Theorem Back in elementary school you learned the Pythagorean Theorem. It says that if you have a RIGHT ANGLED triangle. The square of the hypotenuse is equal to the sum of the squares of the other two sides. Here s a diagram to help. The hypotenuse is the longest side of the triangle and is always ACROSS from the marked right angle.
MFM 2P U1L5 Pythagorean Theorem Example 1. Using Pythagorean Theorem to find the Hypotenuse Example 2. Using Pythagorean Theorem if Given the Hypotenuse This time we are given the value across from the right angle which we will fill in for c. The other value is filled in for EITHER a or b. It doesn t matter which. I ve used a in this question. Example 3. Using Pythagorean Theorem in a problem question. A roof truss is shown. If the house is going to be 8 m and the roof will have a rise of 3 m how long is the slanted portion of the truss? Practice Questions Page 49 #1, 2a)b) 3a)b) 4, 5, 7, 8, 11, 13
U1L5 Primary Trig Ratios.notebook Today's Topic : the primary trig ratios Today's Goal : I can use the three primary trig ratios to solve for sides and angles in right triangles. The Three Primary Trig Ratios opposite adjacent hypotenuse θ The three primary ratios mean nothing without an angle reference. Without the angle reference you do not know which side of the triangle is opposite and which is adjacent. The first step in all trig problems is to identify the angle you either need to use, or you have to find. In the above diagram our reference angle is marked as θ. The three primary trig ratios are as follows... sine θ cosine θ tangentθ Example 1. State the three primary trig ratios for the two angles in the given triangle. Leave your answer as a fraction (in lowest terms if necessary). Example 2. Use your calculator to find the following... a) tan 45 o = b) cos 53 o = c) sin 78 o = Example 3. Use your calculator to solve for the angle... a) sin A=0.5673 b) tan B=0.5673 Example 4. Using Trig Ratios to Find Angles in a Right Triangle 1
U1L5 Primary Trig Ratios.notebook Example 5. Using Trig Ratios to Find Sides in a Right Triangle TIPS * always chose the angle you are using or finding, then label (from the angle) all sides (opposite, adjacent or hypotenuse). * cross out the side that you don't need to use (you don't have the side and you don't want it.) * Decide which ratio uses the two remaining sides. * Set up and solve your proportion. * When you are finding an angle you need to use the inverse buttons (ie. shift tan, to give tan 1 ). When you are finding a side, you will have to set up and solve a ratio for the missing variable. 2
U1L6 Applications of Primary Trig Ratios.notebook Today's Topic: Primary Trig Ratios Today's Goal: to learn terminology related to application question and to be able to effectively use trigonometry to solve problems. Applications Using Trigonometry Angle of Depression: Angle of Elevation: Example 1. A helicopter spots a campfire at an angle of depression of 15 o. Draw a diagram and mark on the angle of depression. Example 2. Kaitlin looks up at an angle of elevation of 75 o to see the top of the CN Tower. Draw a diagram and mark on the angle of elevation. Example 3. A surveyor measures the angle of elevation from his eye to the top of a tree to be 73 o. He knows that his eye is 162cm above ground level and he is standing 7 m from the tree when he takes his measurement. How tall is the tree? 1
U1L6 Applications of Primary Trig Ratios.notebook Example 4. A guy wire holds a hydro pole into an upright position. It is attached to the pole at a location 0.5 m from the top, and makes a 63 o angle of elevation with the ground. If the guide wire is 6 m long, how tall is the pole? 2