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ACT Review Worksheet – Trigonometry Name: ___________________________________ 36. What is the cosine of angle A in right triangle ABC below? 2 58. A 8-foot ladder leaning against the wall makes a 60 angle with the floor. What is the height H of the ladder where it touches the wall? F. 5 2 G. 3 5 H. 3 5 J. 2 3 F. 8 sin 60 G. 8 cos 60 H. 8 tan 60 J. 8 sin 60 K. 5 K. 24. For right triangle RST shown below, what is tan R ? F. r s G. r t H. t r J. t s K. s t 8 cos 60 22. An object 4 feet tall casts a 3-foot shadow when the angle of elevation of the sun is what is tan( 3 F. 4 G. 1 H. 4 3 J. 7 K. 12 43. Based on the triangle shown below, what is cos y? 3 4 3 4 5 A. B. C. D. E. 5 5 4 3 3 45. The sides of a triangle are 5, 12 and 13 inches long. What is the angle between the 2 shortest sides? A. 30 B. 45 C. 60 D. 90 E. 120 12 5 34. If sin 13 and cos = 13 , then tan F. J. 5 12 7 13 G. 12 5 K. 17 13 H. 60 13 40. CD is an altitude of equilateral triangle ABC. If CD is 6 3 units long, how many units long is AC ? F. 3 3 G. 6 H. 12 J. 12 3 K. 36 50. In the right angle triangle below, if C has a sine of, 2 a cosine of 29 5 , and a tangent of 2 , how many 5 29 inches long is AB ? F. 50. In ABC , shown below, the measure of B is 41º, the measure of C is 34º, and AB is 25 units long. Which of the following is an expression for the length, in units, of BC ? (Note: The law of sines states that, for any triangle, the ratios of the sines of the interior angles to the lengths of the sides opposite those angles are equal.) 2 5 G. 6 H. J. 12 5 12 K. A. B. 29 30 C. 29 D. E. 1 If tangent of an angle is , what is the cosine of 57. 2 the same angle? 5 A. 2 2 1 B. 2 1 C. 5 2 5 D. 5 2 E. 3 47. From a hot air balloon, the angle between a radio antenna straight below and the base of the library downtown is 57 . If the distance between the radio antenna and the library is 1.3 miles, how many miles high is the balloon? 25 sin 105 sin 41 25 sin 105 sin 34 25 sin 34 sin 75 25 sin 75 sin 41 25 sin 41 sin 105 52. A surveyor took and recorded the measurements shown in the figure below. If the surveyor wants to use these 3 measurements to calculate the length of the pond, which of the following would be the most directly applicable? F. The ratios for the side lengths of 30º-60º-90º triangles G. The ratios for the side lengths of 45º-45º-90º triangles H. The law of cosines: For any ABC , where a is the length of the opposite A , b is the length of the opposite B , and c is the length of the side opposite C , a b c 2bc cos(A) J. The Pythagorean theorem K. A formula for the area of a triangle 2 FG A. 1.3 sin 57 B. 1.3 tan 57 1.3 C. sin 57 D. 1.3 cos 57 E. 1.3 tan 57 2 2 ANSWERS: 36H 24G 43A 34G 58F 22H 45D 40H 50H 57D 47E 50B 52H