Chapter 9 Party Planner

Transcription

1 Name: Date:. Given A 53, B 78, and a 6., use the Law of Sines to solve the triangle for the value of b. Round answer to two decimal places. C b a A c b sin a B sin A b 6. sin 78 sin 53 6.sin 78 b sin 53 b 7.47 B. Given C 7, B 34, and c 5, use the Law of Sines to solve the triangle for the value of a. Round answer to two decimal places. A BC 80 A80 BC A A 9 a sin c A sin C a 5 sin 9 sin 7 5sin 9 a sin 7 a 6. Page

2 3. Given A 7, b 9, and a 7, use the Law of Sines to solve the triangle (if possible) for the value of c. If two solutions exist, find both. Round answer to two decimal places. Pay attention to the directions and the words If two solutions exist.this is a warning that you are looking at SSA, which we learned may result in two different triangles, one triangle or even NO triangles. Start with a picture: IMPORTANT: Determine the height of the triangle. h 9sin 7 h.63 Since ma90 and we are looking for TWO possible triangles. A sketch of each is advised. CASE : B sin A sin b a sin B sin sin7 sin B 7 9sin7 B sin 7 B.08 C C c sin 7 sin sin 40.9 c sin 7 c 5.09 (Continued) Page

3 CASE : In case, the measure of angle B is the supplement to.08 degrees (linear pairs). B B 57.9 C C c sin 7 sin sin 5.08 c sin 7 c. Therefore, the two solutions are c.,5.09. NOTE: Back in step, if we had found the length of the side opposite the given angle equaled the height, we would have only one triangle to solve. Additionally, if the height was larger than the opposite side, then there is no triangle that could be formed. Page 3

4 4. A straight road makes an angle, A, of 0 with the horizontal. When the angle of elevation, B, of the sun is 59, a vertical pole beside the road casts a shadow 6 feet long parallel to the road. Approximate the length of the pole. Round answer to two decimal places. The red markings were added to the picture. The Law of Sines can now be used to find the height of the pole. pole 6 sin 39 sin 3 pole 6sin39 sin 3 pole 7.33 feet Page 4

5 5. After a severe storm, three sisters, April, May, and June, stood on their front porch and noticed that the tree in their front yard was leaning 3 from vertical toward the house. From the porch, which is 08 feet away from the base of the tree, they noticed that the angle of elevation to the top of the tree was. Approximate the height (length) of the tree. Round answer to two decimal places. Note: the phrasing of the question should be changed from height of the tree to length of the tree. As before, start with a sketch: 08 tree sin 7 sin 08sin tree sin 7 tree 4.79 feet Page 5

6 6. Given a 4, b 3, and c, use the Law of Cosines to solve the triangle for the value of A. Round answer to two decimal places. C b a A c B Figure not drawn to scale bc cos A a b c a b c bc A cos bc cos A b c a cos b c a A bc b c a A bc A cos cos cos 3 4 / 3 Ti-83s need parenthesis A A Given C 09, a 8, and b 7, use the Law of Cosines to solve the triangle for the value of c. Round answer to two decimal places. cos c a b bc C c a b bc C c.3 cos cos 09 c Page 6

7 8. In the figure below, a 8, b, and d 4. Use this information to solve the parallelogram for. The diagonals of the parallelogram are represented by c and d. Round answer to two decimal places. a c d b figure not drawn to scale NOTE: The diagonal s entire length is 4 units. Also, and are the measures of the angles formed by the sides of the parallelogram. Also recall consecutive angles of a parallelogram are supplementary. Consider the following picture with important information highlighted: Use the law of cosines to find the measure of then subtract from 80 to find, (again consecutive angles of a parallelogram are supplementary.) 8 4 cos Page 7

8 9. A vertical pole 8 feet tall stands on a hillside that makes an angle of 4 with the horizontal. Determine the approximate length of cable that would be needed to reach from the top of the pole to a point 58 feet downhill from the base of the pole. Round answer to two decimal places. Since the hillside makes and angle of 4 degrees with horizontal, start your drawing with a hill that is inclined 4 degrees. Add the rest of the parts described in the problem to your picture. (green and blue below) Next throw in the red perpendicular lines at B that give you a line parallel to horizontal through B. By alternate interior angles we see a portion of angle B is 4 degrees and the other portion is 90 degrees. Therefore: B = 04 degrees. We can now use the law of cosines to find the length of the wire. b b 70.4' cos 04 Page 8

9 0. A triangular parcel of land has sides of lengths 50, 50, and 650 feet. Approximate the area of the land. Round answer to nearest foot. The area of a triangle formula is Area sin bc A Note the SAS format of the area formula s requisite information. We will need the measure of an angle between two of the sides. Therefore, we start with the law of cosines. We can now use our area formula: A cos A Area bcsin A Area 50650sin Area 6, 0 ft Page 9

10 . Determine the quadrant in which the angle lies. (The angle measure is given in radians.) 3 7 Once again, a picture will help. Notice the relationship between the given fraction and the quartile cutoff at 3.5. Clearly, the angle is to be found in quadrant IV. 7. Determine the area of a triangle having the following measurements. Round your answer to two decimal places. A30, b8, and c 4 Area bcsin A Area 84sin 30 Area 84sin 30 Area 4.90 units Page 0

11 Answer Key. b a c. and feet feet feet 0. 6,08 ft. IV sq. units Page