Finding unknown triangle angles Finding complementary angles Finding supplementary angles Finding vertical angles
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1 Math 154 Chapter 3.3: Solving Geometric Problems Objectives: Finding unknown sides of triangles Finding unknown sides of rectangles Finding unknown sides of bookshelves Finding unknown triangle angles Finding complementary angles Finding supplementary angles Finding vertical angles Finding Unknown Sides of Triangles Ex: An isosceles triangle has two equal sides. If one side of the triangle is 5 inches longer than the other two equal sides and the is 32 inches, find the length of each of the sides. P = side + side + side length of two equal length of two equal length of other side 9 inches = length of two equal sides 14 inches = length of one side 1. One side of a triangle is three times the shortest side. The third side is 7 ft. more than the shortest side. The is 62 ft. Find all three sides. Let = Then = And = shorest side one side third side 11 feet = the shortest side 33 feet = the one side 18 feet = the third side
2 Finding Unknown Sides of Rectangles Ex: Find the width and length of a rectangle if the width is 3 ft. less than twice its length and the is 36 ft. P = 2l + 2w 2 times the length 2 times the width 7 feet = length 11 feet = width 1. Find the width and length of a rectangle if the length is 7 cm. more than twice the width and the is 44 cm. P = 2l + 2w 2 times the length 2 times the width 5 cm = width 17 cm = length
3 Finding Unknown Sides of Rectangles Ex: Find the width and length of a rectangle if the width is one-third the length and the is 160 ft. P = 2l + 2w 2 times the length 2 times the width 60 feet = length 20 feet = width 1. Find the width and length of a rectangle if the length is four-thirds the width and the is 126 cm. P = 2l + 2w 2 times the length 2 times the width 27 cm = width 36 cm = length
4 Finding Unknown Sides of Bookcases Ex: A bookcase is to have 4 shelves, including the top. The height of the bookcase is to be 5 feet more than three times the width. Find the width and height, if only 40 feet of lumber is available. 4 widths 2 heights total 3 feet = the width of the bookcase 14 feet = the height of the bookcase 1. Say you wanted to put up a fence next to a river as shown. The length of the fence is 7 feet more than twice the width. If you only have a total of 104 feet of fencing, what is length and width of the fence? 6 widths 2 lenghts total Answers: 9 feet = the width of the fence 25 feet = the length of the fence
5 Finding Unknown Triangle Angles *Note: The sum of all angles = 180 Ex: One angle in a triangle measures twice the smallest angle, and the largest angle is six times the smallest angle. Find the measures of all three angles. Let = Then = And = smallest angle one angle largest angle sum of all angles 20 = smallest angle 40 = one angle 120 = the largest angle 1. A right triangle has one acute angle twice as large as another acute angle. Find the measure of the two acute angles. right angle another angle one angle sum of all angles 30 = another acute angle 60 = one acute angle
6 Finding Complementary Angles *Note: The sum of complementary angles = 90 Example: Ex: If angle A and angle B are complementary angles, and angle A is 9 less than twice angle B, find the measures of the two angles. measure of angle B measure of angle A sum of all angles 33 = the measure of angle B 57 = the measure of angle A 1. If angle A and angle B are complementary angles, and angle A is 6 more than three times angle B, find the measures of the two angles. measure of angle B measure of angle A total of the angles Answers: 21 = the measure of angle B 69 = the measure of angle A
7 Finding Supplementary Angles *Note: The sum of supplementary angles = 180 Example: Ex: If angle A and angle B are supplementary angles, and angle B is 15 less than twice angle A, find the measures of the two angles. measure of angle A measure of angle B total of the angles 65 = the measure of angle A 115 = the measure of angle B 1. If angle A and angle B are supplementary angles, and angle B is 12 more than three times angle A, find the measures of the two angles. measure of angle A measure of angle B total of the angles Answers: 42 = the measure of angle A 138 = the measure of angle B
8 Finding Vertical Angles *Note: Vertical angles are equal to each other Example: a = b Ex: If angle A and angle B are vertical angles, and angle A and angle B are as marked, find the measures of the two angles. Let = the measure of angle A And = the measure of angle B ( 6 6 x) 2 o measure of angle A measure of angle B o (3x 6) 24 = the measure of angle A 24 = the measure of angle B 1. If angle A and angle B are vertical angles, and angle A and angle B are as marked, find the measures of the two angles. Let = the measure of angle A And = the measure of angle B measure of angle A measure of angle B ( 4x 19) ( 6x 5) Answers: 67 = the measure of angle A 67 = the measure of angle B
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