B Apply

Sketch a right triangle with θ theta as the measure of one acute angle. Find the other five trigonometric ratios of θ . theta .

26. sin   θ = 3 8 sine theta equals . 3 eighths
27. cos θ = 7 20 cosine theta equals , 7 twentieths
28. cos θ = 1 5 cosine theta equals . 1 fifth
29. tan θ = 24 7 tangent theta equals , 24 over 7
30. sec θ = 16 9 secant theta equals , 16 over 9
31. cot θ = 5 4 co-tangent theta equals . 5 fourths
32. sin   θ = 0 . 35 sine theta equals 0 . 35
33. csc θ = 5 . 2 co-secant theta , equals 5 . 2

34. Think About a Plan A radio tower has supporting cables attached to it at points 100 ft above the ground. Write a model for the length d of each supporting cable as a function of the angle θ theta that it makes with the ground. Then find d when θ = 60 ° theta equals 60 degrees and when θ = 50 ° . theta equals 50 degrees .

    

    • Which trigonometric function applies?
    • How do you set up the equation?
35. Indirect Measurement You are 330 ft from the base of a building. The angles of elevation to the top and bottom of a flagpole on top of the building are 55 ° 55 degrees and 53 ° . 53 degrees . Find the height of the flagpole.
36. A 150-ft redwood tree casts a shadow. Express the length x of the shadow as a function of the angle of elevation of the sun θ . theta . Then find x when θ = 35 ° theta equals 35 degrees and θ = 70 ° . theta equals 70 degrees .
37. Geometry An altitude inside a triangle forms 36 ° 36 degrees and 42 ° 42 degrees angles with two of the sides. The altitude is 5 m long. Find the area of the triangle.

In Δ ABC , ∠ C cap delta is a right angle. Two measures are given. Find the remaining sides and angles. Round your answers to the nearest tenth.

38. b = 8 , c = 17 b equals 8 comma c equals 17
39. a = 7 , b = 10 eh equals 7 comma b equals 10
40. m ∠ A = 52 ° , c = 10 m angle eh equals , 52 degrees comma , c equals 10
41. m ∠ A = 34 . 2 ° , b = 5.7 m angle eh equals . 34 . 2 degrees comma . b equals 5.7
42. m ∠ B = 17 . 2 ° , b = 8.3 m angle b equals . 17 . 2 degrees comma . b equals 8.3
43. m ∠ B = 8 . 3 ° , c = 20 m angle b equals . 8 . 3 degrees comma . c equals 20
44. 1. In Problem 5, use the Pythagorean Theorem to find GH.
    2. Multiple Representations Use a trigonometric ratio to find GH.
45. Open-Ended If sin θ = 1 2 , sine theta equals , 1 half , comma describe a method you could use to find all the angles between 0 ° 0 degrees and 360 ° 360 degrees that satisfy this equation.
46. Reasoning Show that cos A defined as a ratio equals cos θ cosine theta using the unit circle.

Use the definitions of trigonometric ratios in right Δ ABC cap delta to verify each identity.

C Challenge

47. sec A = 1 cos A secant eh equals . fraction 1 , over cosine eh end fraction
48. tan A = sin A cos A tangent eh equals . fraction sine eh , over cosine eh end fraction
49. cos 2 A + sin 2 A = 1 cosine squared eh plus , sine squared eh equals 1

50. Geometry A regular pentagon is inscribed in a circle of radius 10 cm.

    

    1. Find the measure of ∠ C . angle c .
    2. Find the length of the diagonal PS. (Hint: First find RS.)

Table of Contents