Plane Trigonometry PDF

Plane Trigonometry 8. Sin A cos B – cos A sin B is equivalent to: Prepared by: Engr. Arnaldo Valino a. Cos (A-B) Reference: Prime Review Center...

Plane Trigonometry 8. Sin A cos B – cos A sin B is equivalent to: Prepared by: Engr. Arnaldo Valino a. Cos (A-B) Reference: Prime Review Center b. Sin (A-B) c. Tan (A-B) 1. How many degrees is 4800 mils? d. Cot (A-B) a. 270 deg 9. A man, who can row 6 km/hr in still water, heads b. 90 deg directly across the current of a river flowing at the rate c. 180 deg of 4.5 km/hr. Find the actual rate and direction of his d. 215 deg motion. 2. The radius of the circle whose arc of length 15 cm a. 7.5 km/hr at 53.13 deg makes an angles of ¾ radian at the center is b. 8.5 km/hr at 54.14 deg a. 10 cm c. 4.5 km/hr at 53.13 deg b. 11.25 cm d. 6.5 km/hr at 54.14 deg c. 20 cm 10. A right triangle whose length of sides may be d. 22.5 cm expressed as ratio of integral units. 3. If sin A = 2.511x, cos A = 3.06x and sin2A = 3.939x, a. Pedal Triangle find the value of x? b. Isosceles Triangle a. 0.265 c. Scalene Triangle b. 0.256 d. Primitive Triangle c. 0.562 11. The triangle with minimum perimeter but maximum d. 0.625 area inscribed in another triangle is known as 4. Solve for x if tan 3x = 5 tanx a. Pedal Triangle a. 20.705 deg b. Euclid’s Triangle b. 30.705 deg c. Primitive Triangle c. 15.705 deg d. None of the above d. 35.705 deg 12. If the sides of the triangle are 2𝑥 +.3, 𝑥 2 + 3𝑥 + 5. If tan x = 1/2 , tan y = 1/3, what is the value of tan (x 3, 𝑎𝑛𝑑 𝑥 2 + 2𝑥, find the greatest interior angle of the +y) triangle. a. 1 a. 100 deg b. 2 b. 120 deg c. 3 c. 60 deg d. 4 d. 160 deg 6. A PLDT tower and a monument stand on a level plane. 13. Given the sides of a triangle as 3m and 5m. The third The angle of depression of the top and bottom of the side is monument viewed from the top of the PLDT tower are a. Between 3m and 8m 13 deg and 35 deg, respectively. The height of the b. From 3m to 7m tower is 50m. Find the height of the monument. c. Greater than 8m a. 33.51 m d. From 2m to 8m b. 7.58 m 14. 14. Given the triangle ABC in which A= 30°30', b= c. 47.3 m 100 m and c = 200 m. Find the length of the side a. d. 30.57 m a. 124.64 m 7. A triangle inscribed in a given triangle whose vertices b. 130.50 m are the feet of the three perpendiculars to the sides c. 142.24 m from the same point insie, the given triangle. d. 103.00 m a. Inscribed triangle 15. An isosceles right triangle has a perimeter of 17.071. b. Primitive Triangle Compute the area of the triangle in square units. c. Pedal Triangle a. 11.5 d. Obtuse Triangle b. 10.5 c. 15.5 d. 12.5 16. The area of an isosceles triangle is 36 m2 with 30° as 24. If two triangles have congruent bases, then the ratio the included angle of the two adjacent equal sides. of their areas equals the ratio of Compute the perimeter of the triangle. a. their perimeter a. 30.21 b. their sides b. 33.12 c. the lengths of their altitudes c. 24.57 d. none of the above d. 35.67 25. Which of the following cannot be an oblique angle? 17. To determine the width of a river a surveyor measures a. acute a line AB 120 m long on one bank. To a point C on the b. obtuse other bank he determines the angle BAC = 48°36' and c. reflex the angle ABC = 54°42'. Find the width of the river. d. right a. 55.7 26. In an isosceles right triangle, the hypotenuse is _____ b. 70.3 times as long as each of the legs. c. 75.5 a. √2 d. 45.3 b. √3 18. The angle which the line of sight to the object makes c. 2 with the horizontal is above the eye of an observer. d. 3 a. Angle of depression 27. Which of the following is not a secondary part of a b. Angle of elevation triangle? c. Acute angle a. Altitudes d. Bearing b. Medians 19. The intersection of the medians of the triangle is c. Exterior angles called: d. Sides a. Midpoint 28. Which is true regarding the signs of the natural b. centerpoint functions for angles between 90° and 180°. c. incenter a. The tangent is positive d. orthocenter b. The cotangent is positive 20. The angle which the line of sight to the object makes c. The cosine is negative with the horizontal is below the eye of an observer. d. The sine is negative a. Angle of depression 29. Which of the following is not a property of a b. Angle of elevation triangle? c. Acute angle a. The sum of the three angles is always equal d. Bearing to two right angles. 21. The line in which the midpoint, orthocenter, b. The sum of two sides is less than the third circumcenter and the ninepoint center lie. side. a. bisector c. If the two sides are equal, the angles b. perpendicular bisector opposite are unequal. c. Euler's line d. The altitudes of the triangle meet in a point. d. median 30. It refers to the angle between any two radii. 22. What is the intersection of the angle bisectors of a a. central angle triangle? b. azimuth a. incenter c. polar angle b. circumcenter d. normal c. orthocenter 31. The angle or inclination of ascend of a road having d. midpoint 8.25% grade is degrees? 23. A triangle with no side equal is known as a. 1.72 a. acute triangle b. 4.27 b. oblique triangle c. 5.12 c. equilateral triangle d. 4.72 d. scalene triangle 32. It refers to a geometric figure which is drawn around 40. 40. An oblique triangle is inscribed in a circle. If one and enclosing another geometrical figure. side of the triangle has a length of 5 cm and the angle a. circumscribed subtended by the side is 15 deg., determine the area b. inscribed of the circle. c. escribed a. 293.12 𝑚2 d. secant b. 160.57 𝑚2 33. It refers to a continuous curve whose endpoints c. 213.43 𝑚2 coincide. d. 123.43 𝑚2 a. Circle 41. What is the sum of the squares of the sine and cosine b. Continuous curve of an angle? c. convergence a. 0 d. closed curve b. 1 34. It refers to a single line which forms a tangent to two c. √3 or more separate curves. d. 2 a. common secant 42. If the coversed sin 𝜃 = 0.134, what is the value of 𝜃? b. common tangent a. 60° c. chord b. 30° d. axis c. 45° 35. A parcel of land in the form of a triangle has sides d. 360° 312 m and 485 m long respectively. The included 43. A surveyor's transit set up 112.1 feet from the base of angle is 81°30'. Find the area of the land. a vertical chimney reads 32° 30' with the cross hairs a. 74,824.11 sq. m. set on the top of the chimney. With the telescope b. 47,895.23 sq. m level, the vertical rod at the base of the chimney is c. 80,543.02 sq.m. 5.1 feet. Compute the height of the chimney? d. 34.,456.07 sq.m. a. 66.3 ft 36. Find the radius of the. circumcircle of the triangle for b. 71.4 ft which A = 56°, B = 24° and a = 67. c. 76.5 ft a. 40.41 d. 170.9 ft b. 30.45 44. Any lines segment joining a vertex of a triangle to a c. 34.56 point on the opposites side d. 43.57 a. median 37. The sides of a triangular grass plot are 20.4 m, 28.5 m b. secant line and 32.6 m, respectively. A goat is tethered to a stake c. cevian within the plot. Find the minimum length of the rope d. euclidian line tied so the goat so that it can graze over the entire 45. If 𝑡𝑎𝑛(2𝐷 − 3) = 1/(𝑡𝑎𝑛(5𝐷 − 9)), determine D in plot. degrees. a. 12.54 a. 14.57 deg b. 15.67 b. 15.30 deg c. 16.47 c. 18.88 deg d. 17.27 d. 16.97 deg 38. What is the value of x if 𝑎𝑟𝑐𝑡𝑎𝑛 𝑥 = 2 𝑎𝑟𝑐𝑠𝑖𝑛 𝑥 ? 46. Evaluate 𝑎𝑟𝑐𝑐𝑜𝑡[2𝑐𝑜𝑠(𝑎𝑟𝑐𝑠𝑖𝑛0.5)]. a. 0.645 a. 30 deg b. 0 b. 45 deg c. 0.345 c. 60 deg d. 0.392 d. 90 deg 1 39. 39. If 𝑠𝑒𝑐2𝐴 = 𝑠𝑖𝑛13𝐴, determine the angle A in 47. Simplify sin2 15° + sin2 75. degrees. a. 0 a. 5 degrees b. Sin30 deg b. 6 degrees c. 1 c. 3 degrees d. sin60 deg d. 7 degrees 48. Given a triangle with an angle C = 28.7°, side a = 132 54. Each interior angle of an equilateral triangle is equal units and side b=224 units. Solve for the side c. to a. 95 units a. 30o b. 125.4 units b. 60 o c. 110 units c. 90 o d. 90 units d. 45 o 49. Simplify {𝑐𝑜𝑠𝐴/[𝑠𝑖𝑛𝐴 + 1]} + 𝑡𝑎𝑛𝐴. 55. From a point outside of an equilateral triangle, the a. secA distances to the vertices are 10m,18m and 10 m b. cscA respectively. What is the length of one side of a c. sinA triangle? d. cosA a. 11.23 or 19.95 50. Points A and B are 100 m apart and are of the same b. 10.94 94 18.64 elevation as the foot of the tower. The angles of c. 12.24 or 4 19.62 elevation of the top of the tower from the points A d. 13.25 or 19.83 and B are 21 degrees and 32 degrees respectively. 56. The sides of a triangle are 8 cm. 10cm. and 14 cm. How far is A from the tower in meters? Determine the radius of the inscribed and a. 259.28 circumscribing circle. b. 265.42 a. 2.45, 7.14 c. 271.62 b. 2.72, 8.21 d. 277.92 c. 3.02, 6.82 51. A man finds the angle of elevation of the top of a d. 3.26, 7.82 tower to be 30 degrees. He walks 85 m nearer the 57. The area of the inner triangle ABC is 4 that of tower and finds its angle of elevation to be 60 triangle ADE. AB=45 m., AD=65 m., AE=90 m. degrees. What is the height of the tower? Point B is along line AD and point C is along line a. 76.31 m AE. Find the length of the segment CE? b. 73.31 m a. 62.4 c. 73.16 m b. 57.5 d. 73.61 m c. 49.2 52. A and B are summits of two mountains rise from a d. 71.8 horizontal plain. B being 1200m above the pain. Find 58. If the sides of a parallelogram and an included angle the height of A, it being given that its angle of are 6, 10 and 100 degrees respectively, find the length elevation as seen from a point C in the plain (in the of the shortest diagonal. same vertical plane with A and B) is 50 deg, while the a. 10.63 angle of depression of C viewed from B is 28°58' and b. 10.37 the angle subtended at B by AC is 50 deg. c. 10.73 a. 2847.64 m d. 10.23 b. 3200.20 m 59. Solve for 𝜃 in the following equation: 𝑠𝑖𝑛2 𝜃 = c. 2989.42 m 𝑐𝑜𝑠 𝜃. d. 3002.33 m a. 30 deg 53. An observer wishes to determine the height of a b. 60 deg tower. He takes sight at the top of the tower from A c. 45 deg and B, which are 50 ft apart at the same elevation on d. 90 deg a direct line with the tower. The vertical angle at 60. Simplify 4𝑐𝑜𝑠(𝑦) 𝑠𝑖𝑛(𝑦)(1 − 2𝑠𝑖𝑛2𝑦) point A is 30 deg and at point B is 40 deg. What is the a. tan(4y) height of the tower? b. sec(4y) a. 85.60 ft c. cos(4y) b. 143.97 ft d. sin(4y) c. 110.29 ft 61. The series expansion for cos x contains which powers d. 92.54 ft of x? a. 0, 2, 4, 6, 8,... b. 1, 3, 5, 9,... c. 1, 2, 3, 4, 5,... d. 1/2, 3/2, 5/2, 7/2... 62. Find the value of A between 270 deg and 360 deg if 2 sin2 𝐴 − 𝑠𝑖𝑛𝐴 = 1. a. 330 deg b. 340 deg c. 300 deg d. 320 deg 63. A pole cast a shadow 15 m. long when the angle of elevation of the sun is 61 deg. If the pole has lean 15 deg from the vertical directly towards the sun, what is the length of the pole? a. 54.23 m b. 48.64 m c. 36.84 m d. 64.84 m 64. Which of the following is the value of 1 radian in degrees? a. 89.55° b. 60.3° c. 57.3° d. 45.58° 65. Three forces 20 N, 30 N and 40 N are in equilibrium. Find the biggest angle formed by these forces. a. 104.48 deg b. 102.36 deg c. 101.42 deg d. 103.21 deg