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the definition of tan 0 m-tan 0, where m is the slope and 0 is the angle of inclination of the line. The following exercises, which depend on properties of triangles, refer to triangle ABC in the figure on the righ Exercises 77-82 in order Assume that all angles are measured in degrees Av tan 0- tan 0= m-tan 0 m₂ - m₁ 1+m₁m₂ e a 0 slope - m, a 6/C B ✓ skope - my B 77. In terms of B, what is the measure of angle ABC? 180-B (Do not include the degree symbol in your answer.) 78. Use the fact that the sum of the angles in a triangle is 180° to express 0 in terms of a and B. 0 = 8-a 79. Apply the formula for tan (A-B) to obtain an expression for tan 0 in terms of tan a and tan ß. tan B-tan a 1+ tan ßtan a 80. Replace tan a with m, and tan ẞ with m₂ to obtain an expression for tan 0 in terms of m, and m₂. a Q G 31. Use the result from Exercise 80 to find the acute angle between the pair of lines defined by the equations x+y=7 and 3x+y=-4. The measure of the angle is approximately 26.6° Type an integer or decimal rounded to the nearest tenth as needed.) 32. Use the result from Exercise 80 to find the acute angle between the pair of lines defined by the equations 2x-3y +3=0 and 5x+6y=9. polo ir approximately

the definition of tan 0 m-tan 0, where m is the slope and 0 is the angle of inclination of the line. The following exercises, which depend on properties of triangles, refer to triangle ABC in the figure on the righ Exercises 77-82 in order Assume that all angles are measured in degrees Av tan 0- tan 0= m-tan 0 m₂ - m₁ 1+m₁m₂ e a 0 slope - m, a 6/C B ✓ skope - my B 77. In terms of B, what is the measure of angle ABC? 180-B (Do not include the degree symbol in your answer.) 78. Use the fact that the sum of the angles in a triangle is 180° to express 0 in terms of a and B. 0 = 8-a 79. Apply the formula for tan (A-B) to obtain an expression for tan 0 in terms of tan a and tan ß. tan B-tan a 1+ tan ßtan a 80. Replace tan a with m, and tan ẞ with m₂ to obtain an expression for tan 0 in terms of m, and m₂. a Q G 31. Use the result from Exercise 80 to find the acute angle between the pair of lines defined by the equations x+y=7 and 3x+y=-4. The measure of the angle is approximately 26.6° Type an integer or decimal rounded to the nearest tenth as needed.) 32. Use the result from Exercise 80 to find the acute angle between the pair of lines defined by the equations 2x-3y +3=0 and 5x+6y=9. polo ir approximately

Trigonometry (11th Edition)
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.
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Refer to the figure on the left below. By the definition of tan 0, m-tan 0, where m is the slope and 0 is the angle of inclination of the line. The following exercises, which depend on properties of triangles, refer to triangle ABC in the figure on the right below Work Exercises 77-82 in order Assume that all angles are measured in degrees. tan 0 = tan 0= m- tan 0 m₂ - m₁ 1+m₁m₂ 0 0 slope = m₁ A б/с 77. In terms of ß, what is the measure of angle ABC? 180-B (Do not include the degree symbol in your answer.) 78. Use the fact that the sum of the angles in a triangle is 180° to express 0 in terms of a and B. 0= ß-a 79. Apply the formula for tan (A-B) to obtain an expression for tan 0 in terms of tan a and tan ß. tan ß - tan a 1 + tan ẞ tan a 80. Replace tan a with m₁ and tan ß with m₂ to obtain an expression for tan 0 in terms of m₁ and m₂. B slope = m₂ B 81. Use the result from Exercise 80 to find the acute angle between the pair of lines defined by the equations x+y=7 and 3x+y = - 4. The measure of the angle is approximately 26.6° (Type an integer or decimal rounded to the nearest tenth as needed.) 82. Use the result from Exercise 80 to find the acute angle between the pair of lines defined by the equations 2x-3y +3=0 and 5x+6y= 9. The measure of the angle is approximately (Type an integer or decimal rounded to the nearest tenth as needed.)
Transcribed Image Text:Refer to the figure on the left below. By the definition of tan 0, m-tan 0, where m is the slope and 0 is the angle of inclination of the line. The following exercises, which depend on properties of triangles, refer to triangle ABC in the figure on the right below Work Exercises 77-82 in order Assume that all angles are measured in degrees. tan 0 = tan 0= m- tan 0 m₂ - m₁ 1+m₁m₂ 0 0 slope = m₁ A б/с 77. In terms of ß, what is the measure of angle ABC? 180-B (Do not include the degree symbol in your answer.) 78. Use the fact that the sum of the angles in a triangle is 180° to express 0 in terms of a and B. 0= ß-a 79. Apply the formula for tan (A-B) to obtain an expression for tan 0 in terms of tan a and tan ß. tan ß - tan a 1 + tan ẞ tan a 80. Replace tan a with m₁ and tan ß with m₂ to obtain an expression for tan 0 in terms of m₁ and m₂. B slope = m₂ B 81. Use the result from Exercise 80 to find the acute angle between the pair of lines defined by the equations x+y=7 and 3x+y = - 4. The measure of the angle is approximately 26.6° (Type an integer or decimal rounded to the nearest tenth as needed.) 82. Use the result from Exercise 80 to find the acute angle between the pair of lines defined by the equations 2x-3y +3=0 and 5x+6y= 9. The measure of the angle is approximately (Type an integer or decimal rounded to the nearest tenth as needed.)
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