Review Journal 7 Page 57

Transcription

1 Student Checklist Unit 1 - Trigonometry 1 1A Prerequisites: I can use the Pythagorean Theorem to solve a missing side of a right triangle. Note p. 2 1B Prerequisites: I can convert within the imperial and metric systems. Side Lengths: I can use primary trig ratios to determine the side lengths of right triangles. Angles: I can use primary trig ratios to determine the side lengths of right triangles. Applications: I can use primary trig ratios to solve word questions Obtuse Angles: I can calculate obtuse angles using supplementary angle theorem. Sine Law: I can use the sine law to calculate angles and sides in non-right triangles. Cosine Law: I can use the cosine law to calculate angles and sides in non-right triangles. Problem Solving I can determine whether to use SOH CAH TOA, Sine Law or the Cosine Law to solve triangles. Note p.3 and worksheet Note Review Journal 7 Page 57 p8 # 2-4 Journal 1 Note p9 #5,6 Journal 2 Note p9 #7-9,11,12,16 Journal 3 Note p. 19 #2-6 p 23# 5-7, 10 Journal 4 Note p. 31#5,11, 13, Journal 5 Note p. 38 #4, 7, 10, 13, 18 Journal 6 Note p. 47 # 4, 6, 7, 8, 12 Page 54 #1,3,14,18,20,22,26,28

2 1A prerequisite Goal I can use the Pythagorean theorem to solve a missing side of a right triangle. I can convert within the imperial and metric systems. Review of Basic Measurement Pythagorean Theorem need a right angle triangle use it to find a side length Examples: Find the missing side. 1. 2' 5" 31" m 20cm 3. 21ft 15ft

3 1B Preskills Review of Metric Measurement The basic units of metric measurement are: grams mass (weight) litres liquid (volume) metres length Prefixes are added to the above units. The most common are kilo, hecto, deka, deci, centi, and milli. Moving from one "prefix" to the next is 10. ie. multiply/divide by 10. K H D U D C M Kids Hide Dirty under wear Down Covered Manholes When you move When you move x 10 for each prefix 10 for each prefix Metric Conversions Examples: K H D U D C M km to metres ml to litres Examples:

4 1B Preskills Imperial Conversions 1 foot = 12 inches 1 yard = 36 inches 1 yard = 3 feet 1 mile = 5280 feet Shortforms inches in ; " feet ft ; ' yard yd mile mi 1 mile = 1760 yards Examples: 1. 5' 5" to feet yd to mi.

5 2 Side Lengths Goal I can use primary trig ratios to determine the side lengths of right triangles. Primary Trigonometric Ratios The study of trigonometry, is the study of the measurements of triangles. The following is review of what you should already know. The 3 trig ratios are: sine cosine tangent θ Labelling Sides of Triangles Hy O A SOH CAH TOA

6 2 Side Lengths Finding Side Lengths 1. Determine the measure of the missing sides. a) b) 25 o y 88'

7 3 Angles Goal I can use primary trig ratios to determine angles. Using you calculator: Find the following angles: a) sinθ = b) cosθ = c) tanθ = Solving for Angles Example: 1. Determine the measure of angle A.

8 3 Angles 2. 14' x 3yd 3. 3" x 1.5"

9 3 Applications Goal I can use primary trig ratios to solve real world type questions. Applications Terminology Often surveyors use the angle of elevation or the angle of depression to describe positions of objects. The angle of elevation is always measured from the horizontal up. It is always INSIDE the triangle. The angle of depression is always OUTSIDE the triangle. It is never inside the triangle. 1

10 3 Applications Examples: 1. A 6' ladder leans against a wall. The angle formed by the ladder and the ground is 71 o. a) How far is the foot of the ladder from the wall? b) How far up the wall does the ladder reach? 2

11 3 Applications 2. A cabin is 125 m from the base of a 100m cliff. What is the angle of depression from the top of the cliff to the cabin? 3

12 5 Obtuse Angles Goal I can calculate the measure of obtuse angles given the ratio. Obtuse Angles sine, cosine, tangent Investigation: Calculate the following trigonometric ratios to 4 decimal places. sin 25 o = cos 25 o = tan 25 o = The supplementary angle of 25 o = Find the sin, cos, and tan, of the supplementary angle. sin o= cos o= tan o= Choose another acute angle and determine the primary trig ratios. sin o= cos o= tan o= Determine the supplementary of the angle you chose from above. Determine the ratio of the supplementary angle. sin o= cos o= tan o= 1

13 5 Obtuse Angles Conclusions: When a θ is acute, the ratios for sine, cosine, and tangent are When a θ is obtuse (greater than 90 o ), the ratios for sine is cosine is tangent is When converting from a sine ratio to an angle, Examples: 1. State if the ratio will be positive or negative. sin58 o cos152 o cos48 0 tan91 o sin148 o 2. Determine the value(s) of θ. a) cos θ = b) sin θ = c) tan θ =

14 6 Sine Law Goal I can use the Sine Law to solve angles and side lengths in non right triangles. The Sine Law = = OR = = Use the sine law if you have the following: two angles and any side or two sides and the angle opposite one of these sides HINTS: 1. If given 2 angles, calculate the 3rd 2. Check to make sure you have an angle and its opposite side 1

15 6 Sine Law Examples: 1. Solve for s 2. Find the measure of angle θ. a) b) 2

16 7 Cosine Law Goal I can use the Cosine Law to find angles and side lengths in non right triangles. The Cosine Law OR a 2 = b 2 + c 2 2bc cosa Use the cosine law when you know one of the following: The measures of 3 sides The measures of 2 sides and their contained angle Examples: 1. Determine the length of n in MNP. 25cm N 105 o 13cm M n P 1

17 7 Cosine Law 2. Determine the measure of <C in BCD. C 500ft B 750ft 650ft D 3. An air traffic controller at T is tracking two planes, U and V, flying at the same altitude. How far apart are the planes? N 10.7mi U t T 23 o 75o 15.3mi V 2

18 8 Problem Solving Problem Solving Often 2 or more steps may be needed to solve a triangle problem. Sketch a diagram The sum of angles in any triangle is 180 o Right Triangle Oblique Triangle Pythagorean Theorem Primary Trig Ratios Sine Law Cosine Law Examples: 1. 1

19 8 Problem Solving At an excavation site, points A,B, andc have been marked. The measure of angle C is 132 o. Points A and C are 4.2 m apart. Points B and C are 5.7 m apart. How far apart are points A and B? 2