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Foundations and Pre-Calculus Math 10 Name:___________________________ Chapter 2: Trigonometry Assignment Checklist Block:___________________________ Each assignment must have: - Title – section, page number and questions Questions written down Work shown Answers marked Corrections done A mark out of 5 Assignments Section Questions 2.1 The Tangent Ratio Pg 75-77 # 3, 4, 8 – 14, 17 – 21 2.2 Using the Tangent Ratio to Calculate Lengths Pg 82-83 # 3 – 5 (a & c), 6 – 14, 15 2.3 Measuring an Inaccessible Height Project 2.4 The Sine and Cosine Ratios Pg 95-96 # 4 – 10, 12 – 15 2.5 Using the Sine and Cosine Ratios to Calculate Lengths Page 101-102 # 3 – 14 2.6 Applying the Trigonometric Ratios Page 111 # 3 – 14 2.7 Solving Problems Involving More than One Right Triangle Pg 118-121 #3 – 9, 14 Date Assigned Total Please have assignments in this order stapled together with this page on top. Due: _____________________ Mark Ch 2 Glossary Acute angle Adjacent Angle of depression Angle of elevation/inclination Complementary angles Cosine Hypotenuse Inverse Obtuse angle Opposite Pythagorean Theorem Ratio Right Angle Right Triangle Sine Supplementary angles Tangent Trigonometric Ratios Naming the Sides of a Right Triangle TOOLKIT: 2.1 The Tangent Ratio SUMMARY: Recall the three trig ratios: Sin, Cos, Tan SOH CAH TOA Make sure that your calculator is set to degrees If <A is an acute angle in a right triangle, then tan A = opposite adjacent hyp opp A adj 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑠𝑖𝑑𝑒 𝑙𝑒𝑛𝑔𝑡ℎ Tangent Ratio: 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒 𝑙𝑒𝑛𝑔𝑡ℎ To find an angle using the tangent ratio, you must first know the ratio of the opposite and adjacent side (express this as a decimal). Use the 𝑇𝑎𝑛−1 or Inverse Tan button on your scientific calculator – make sure you are in degrees!!! Questions/Main Ideas: Ex 1: In the right triangle, calculate the following: C 11cm B 18cm A A) tan A and < A B) tan C and < C Notes: Ex 2: Ex. Find the angle A) tan A = 0.4 B) tan A = 4/5 C) tan A = 0.9528 Ex 3: Ex 4: A support cable is anchored to the ground 5m from the base of a telephone pole. The cable is 19m long. It is attached at the top of the pole. What angle, to the nearest degree, does the cable make with the ground? Assignment Pearson: Page 75 # 3 & 4, 8 – 14, 17 – 21 TOOLKIT: 2.5 2.2 Sine 2.4 Tangent The Sine and to Cosine and Calculate Cosine to Calculate Ratios Sides Sides SUMMARY: SUMMARY: SUMMARY: RecallCAH SOH the Tangent TOA Ratio from yesterday. x hyp opposite opp opp tan 0.5x hyp Sin AA= adjacent hyp opp A Sin A = 0.5 A adj adj x missing side Coscan A also use the tangent ratio tohyp We find hyp lengths A adj 0.7x Direct Measurement: Use a measuring instrument (protractor, measuring tape etc…) to determine a specific Cos A = 0.7 value (angles or side lengths) **Remember to use shift key for angles** **Remember that you are not using the shift key to find side lengths** Indirect Measurement: use mathematical reasoning and logic to determine specific values (angles or side Questions/Main Ideas: Notes: lengths) Questions/Main Ideas: Notes: Ex. Ex 1: 1:In Calculate triangle the GHJ, following: identify Questions/Main Ideas: the Sin A) following: 43 B) Cos 43 Ex 1: theG; ratio a) Sin G, Cos ∠Glength of Ex. 2:Find Calculate the PQ to J, theCos nearest b) Sin J; ∠Jtenth of a A) cm:tan 16 B) tanP 42 C)Htan 25 J Ex 2: Find the length of XY to 10.4m 15cm the nearest tenth of a cm. 17cm Y 67° R Q 5cm X 70° a radar station, the G From Ex 3: Z angle of elevation of an Ex 2: An observer is sitting on. approaching airplane is 32.5 aThe dock watching a float plane horizontal distance in Harbour. At a between plane and the ExVancouver 3: In the Right triangle PQR, certain time, the plane is 300m radar station is 35.6 km. <R=90, <Q = 25, and PRHow = above theplane waterfrom and 430m far the the radar 7cm.is Determine the length of from the observer. What is the station to the nearest tenth of a QR to the nearest millimeter. angle of elevation of the plane kilometer? measure from the observer, to the nearest degree? Notes: Ex 4: A forest technician is collecting data about the heights of trees. She paces a distance of 15m from the base of the tree and uses a clonometer to measure the angle of elevation to the top of the tree. The angle is 25. The technician’s eye is about 1.5m above the ground. Assume that the ground is level. How tall is the tree? Ex 5: At a horizontal distance of 200m from the base of an observation tower, the angle between the ground and that line of sight to the top of the tower is 8°. How high is the tower to the nearest tenth of a metre. Sketch a diagram to help you solve the problem. Assignment Pearson: Page 82 # 3 – 5 (a & c), 6 – 14, 15 TOOLKIT: TOOLKIT: 2.7 2.6 Solving ApplyingProblems Trig Ratios Involving More than One Right Triangle SUMMARY: Continue Use your trig using tools yourtotrig solve tools: right triangles: Sin, Cos, Tan , Pythagoras and other properties of triangles Sin, Cos, Tan, Pythagoras etc… Remember, draw a model/picture to help you visualize Draw diagrams the problem. where necessary When we are told to “solve” a right triangle, we are being asked to find all unknown measures in that triangle. Questions/Main Ideas: Ex. 1: Two office towers are Questions/Main 50m apart. From theIdeas: 14th floor of tower, the Ex.the 1: shorter Solve triangle ABCangle of elevation to=the top BC of the given that AC 5cm, = taller tower is 33 degrees. The 2cm and <B = 90° angle of depression to the base of the taller tower is 39 degrees. Determine the height of the taller tower. Ex. 2: Solve triangle XYZ given XY = 9m, <Y = 90 and <Z = 36 Ex. 2: As part of a weekend expedition, an Adventurer’s Club proposes to climb a cliff overlooking a river. To plan for the climb, a surveyor took Ex 3: measurements Lighthouse park some to is 7km due north the of Tower in calculate height Beach of the cliff. Vancouver. A sailboat leaves From a point R on the shore Lighthouse Parktheonriver, a bearing directly across the of 211 degrees. When the angle of elevation to the top of sailboat due west of Tower the cliff isis <TRB = 43°. From straight aBeach, point itS,turns 30m down river, towards Howthe far <BSR = the 69°.beach. Calculate does the travel? height ofboat the cliff. Notes: Notes: