Section 3.4 Solving Problems Using Acute Triangles

Transcription

1 Section 3.4 Solving Problems Using Acute Triangles May 9 10:17 AM Example 1: Textbook page 154 Two security cameras in an museum must be adjusted to monitor a new display of fossils. The cameras are mounted 6 m above the floor, directly across from each other on opposite walls. The walls are 12 m apart. The fossils are displayed in cases made of wood and glass. The top of the display is 1.5 m above the floor. The distance from the camera on the left to the centre of the top of the display is 4.8 m. Both cameras must aim at the center of the top of the display. What is the angle of depression for each camera? Jul 5 8:47 PM 1

2 Example 2: The world s tallest free-standing totem pole is located in Beacon Hill Park in Victoria, B. C. While visiting the park, Manuel wanted to determine the height of the totem pole, so he drew a sketch and made some measurements: He paced 42 meters from the totem pole. From that spot, estimated the angle of elevation to the sun to be 40. He observed that the ground was not flat and estimated the angle made with the horizontal to be 5 What is the height of the totem pole to the nearest metre? Jul 5 8:32 PM Example 3: Brendan and Diana plan to climb the cliff at Dry Island Buffalo Jump, Alberta. They need to know the height of the climb before they start. Brendan stands at point B, as shown in the diagram. He uses a clinometer to determine ABC, the angle of elevation to the top of the cliff. Then he estimates CBD, the angle between the base of the cliff, himself, and Diana, who is standing at D. Diana estimates CDB, the angle between the base of the cliff, herself and Brendan. Determine the height of the cliff to the nearest meter. Jul 5 8:34 PM 2

3 A regular octagon is inscribed in a circle of radius 15.8 cm. What is the perimeter, to the nearest tenth of a centimeter, of the octagon? Nov 26 1:23 PM Two support wires are fastened to the top of a communications tower from points A and B on the ground. The points are on opposite sides of the tower and in line. One wire is 18 m long, and the other wire is 12 m long. The angle of elevation of the longer wire to the top of the tower is 38. a) Draw a diagram of the scenario. b) How far apart are points A and B, to the nearest tenth of a metre? Nov 26 1:31 PM 3

4 A smokestack is 150 metres high. Two observers, located at positions S and T, look to the top of the smokestack at angles of elevation of 42 and 25 respectively. How far apart are the two people? Nov 14 2:31 PM Two ships left a harbour together traveling on courses that had an angle of 114.7ο between them. One travelled at 39 mph and the other travelled at 41 mph. After 3 hours, how far apart were the ships? Nov 29 10:12 AM 4

5 Find the values of x and y. Nov 29 10:16 AM Two airplanes leave an airport, and the angle between their flight paths is 40º. An hour later, one plane has traveled 300 miles while the other has traveled 200 miles. How far apart are the planes at this time? Nov 14 2:33 PM 5

6 Two people looked up in the sky and saw an airplane flying. Person A saw the airplane at an angle of elevation of 65 and person B saw it at an angle of elevation of 80. The two people are standing 30 feet from each other. Compute the distance from each person to the airplane. Nov 14 2:34 PM Jill and her friends built an outdoor hockey rink. Their hockey goal line is 5 feet wide. Jill shoots a puck from a point where the puck is 5 yards from one goal post and 6 yards from the other goal post. Within what angle must Jill make her shot to hit the net? Nov 14 2:35 PM 6

7 Two people looked up in the sky and saw superman flying. Person A saw Superman at an angle of elevation of 65 o and person B saw Superman at an angle of elevation of 80 o. The two people are standing 30 feet from each othercompute the distance from each person to superman. Nov 14 2:37 PM A triangular lot sits at the corner of two streets that intersect at an angle of One street of the lot is 32 m and the other is 40 m. How long is the back of the lot (the third side), to the nearest metre? Nov 14 2:38 PM 7

8 To find the height of the cliff that is inaccessible, a surveyor measures a baseline AC of 400m. In the horizontal plane ABC, ÐA=27º and ÐACB = 35º. In the vertical plane BTC, ÐBCT=18º. Determine the cliff height to the nearest metre. Nov 14 2:55 PM Page #'s 2a, 4, 5, 6, 7, 9, 10, 13, 14 Jun 22 8:43 AM 8