From the top of the bridge over the Burlington Canal. Maria looks down at a sailboat at an angle of depression at 15. The bridge is 18 m above the water. Calculate the horizontal distance from the bridge to the sailboat. Hint: This question is similar to question #1.... Draw your sketch first. 0 15 ??? horizontal distance 18 m Problem #7 A rafter makes an angle of 22.5 with the roof joist, as shown. How tall is the board supporting the middle of the roof. How tall is the board supporting the middle of the roof? 22.50 12 ft Project: Lesson 1 Page 10 Problem #3: A wheelchair ramp is needed at the entrance of a restaurant. The ramp is to be 6.10 m long and have a rise of 0.45. Calculate the angle of inclination. 6.10 m long 0.45 m rise ??? angle of inclination Project: Lesson 1 Page 6 Problem #5: A 7.5 m flagpole is 4.6 m away from a pedestrian. What is the angle of elevation from where the pedestrian is standing to the top of the flagpole? 7.6 m angle of elevation ????? 4.6 m Project: Lesson 1 Page 8 Problem #8 From the top of a 200-m high cliff, the angles of depression of two boats on the water are 20 and 25. How far apart are the boats? Hint: This is a three step process. Project: Lesson 1 28 20 200 m cliff Page 11 Angle of Elevation: The angle of elevation (also called the angle of inclination) is the angle that is formed between the horizontal and the sight line form the observer's eye to some object above eye level. For example: Line of Sight Object Horizontal Observer Angle of elevation Angle of Depression: The angle of depression is the angle between the horizontal and the sight line from the observer's eye to a point below the eye level. Project: Lesson 1 Angle of depression Horizontal Observer Line of Sight Object Page 2 Problem #6 A garage floor is made of poured concrete. The length of the garage is 6.7 m and the grade (rise of the floor from front to back) is .09 m. Calculate the angle of inclination. Project: Lesson 1 6.7 m .09 m Page 9 Problem #1: From the top of the Niagara Escarpment, Juan sees a sailboat below at an angle of depression of 40. Juan is approximately 100 m above the car. How far is the sailboat from the base of the escarpment? Round your answer to the nearest metre. 100 m angle of depression 40 777777 40 Project: Lesson 1 Page 4 1 of 11 Project: Lesson 1 Instructions: Complete the following project by writing your full solutions on separate paper. When finished, electronically submit your work into your course dropbox for Lesson 1 Part A Making Decisions Using Trigonometry Carpenters have to calculate the length of lumber support for a roof rafter. Engineers have to determine the angle of elevation or depression when calculating the height of a structure. Pilots use trigonometry to navigate aircraft and to correct for wind effects. Ships' captains do the same for ocean currents. To calculate unknown measurements, these professionals need to decide which trigonometric tool or formula to use. What tools are available?? Pythagorean Theorem: hypotenuse = side1 + side2 Primary Trigonometric Ratios: opposite sin 0 = hypotenuse cos e = adjacent hypotenuse tan e opposite adjacent Project: Lesson 1 Page 1 Problem #2: In construction the pitch of a roof may be given as "7-12" in feet. This means that the maximum height of the roof is 7 ft and the distance from the midpoint of the base of the roof to the outer walls is 12 ft. Calculate the roof's angle of inclination. Round your answer to the nearest degree. Project: Lesson 1 roof slope 7 ft ????? 12 ft angle of elevation Page 5 How do these two angles relate to each other? Since you are working with 2 horizontal lines (which are parallel to each other) and a straight line that connects these two horizontal lines, the angle of depression is equal to the angle of elevation. This relationship can be very useful when solving problems given. Horizontal line Angle of depression Angle of 38 elevation Horizontal line Using these tools Use these tools to solve the following problems. Show your answers in complete steps. Project: Lesson 1 Page 3