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Exercises
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1. Find the perpendicular height of an equilateral triangle with sides of 10-in. a. 6.32 in b. 7.28 in c. 8.66 in d. 9.31 in 2. The angle of elevation of the top of tower B from the top tower A is 30 deg and the angle of elevation of the top of tower A from the base of tower is 45 deg. The two towers lie in the same horizontal plane. If the height of tower B is 130 m, find the height of tower A. a. 82.42 m b. 85.42 m c. 88.52 m d. 80.22 m 3. The horizontal angle from the ground to the top of a pine tree of some unknown distance away is 50 deg. At a point 140 ft directly behind the first point, the horizontal angle to the top of the three is 40 deg. What is the distance from the pine tree to the first point? a. 310.2 ft b. 328.1 ft c. 348.2 ft d. 333.1 ft 4. A transit set up 160 feet from the base of a vertical chimney reads 35 deg with the cross hairs set on the top of the chimney. With the telescope level, the vertical rod at the base of the chimney is 5.8 ft. How tall is the chimney? a. 110.2 ft b. 117.8 ft c. 123.7 ft d. 128.8 ft 5. What is the angle whose tangent is 3 and whose sine is negative? a. 321.3 deg b. 251.6 deg c. 280.4 deg d. 274.3 deg 6. What is the exact value of the secant of acute angle θ. Given that sin θ=4/7? a. 2.32 b. 1.75 c. 1.22 d. 2.12 7. Solve for θ in the following equation: a. 20 deg b. 25 deg c. 30 deg d. 35 deg 8. If sec2x is 7/2, the quantity 1 - sin2x is equivalent to _____. a. 0.381 b. 0.421 c. 0.187 d. 0.286 9. Sin (x – y) is equal to ____, when x=90 deg and y is an acute angle. a. –cos y b. sin y c. –sin y d. cos y 10. What is the simplified expression of equivalent expression of (cot2x)(sin2x)+[1/csc2x]? a. 1 b. -1 c. 0 d. 1/2 11. What is the equivalent expression for cos2θ? a. 1-[2/cos2θ] b. 1+[2/cos2θ] c. 2-[1/cos2θ] d. 2+[1/cos2θ] 12. Three circles of radii 130, 160 and 140 are tangent to one another. What are the interior angles of triangle formed by joining the centers of the circles? a. 54.4o, 65.3o, 60.3o b. 54.4o, 60.9o, 64.7o c. 68.8o 58.5o, 52.7o d. 55.8o, 64.3o, 59.9o 13. Two forces of 30 units and 35 units act on a body. If their directions make an angle of 55 degrees. What is the magnitude of the resultant force? a. 25.2 b. 28.3 c. 30.3 d. 33.3 14. Given C=35 deg, a=156 and b=250. Find the angle B a. 110 deg b. 118 deg c. 123 deg d. 109 deg 15. Given A=48 deg, c=28 and B=72 deg. Find side b. a. 28.2 b. 24.2 c. 30.7 d. 33.8 16. Simplify: secx - (secx)(sin2x) a. –cos x b. cos x c. sin x d. csc x 17. Solve for x: 1.5=[0.0520/x]1.35 a. 0.03851 b. 0.04582 c. 0.05571 d. 0.06811 18. Solve for x: 37.2x=6.45x-3 a. -2.31 b. -3.19 c. -4.22 d. -5.05 19. A car travels 38 kph due east and another car from the same point at N 35 deg E at the rate of 75 kph. After 3 hrs, the distance between two points is ____. a. 180.1 km b. 175.3 km c. 184.9 km d. 188.8 km 20. Town A is 15 miles due west of town B, and town C is 13 miles die south of town B. How far is it from town A to town C? Assuming straight roads connecting the three towns, what is the angle at A between the roads leading to B and C? a. 33.6 deg b. 36.2 deg c. 38.6 deg d. 40.9 deg 21. From a point on the ground 160 ft from the base of a building, the angle of elevation of the top of the building is 64.3 deg. How high is the building? a. 300.0 ft b. 332.5 ft c. 354.8 ft d. 360.8 ft 22. Solve for x if log x + log (x – 24) = 2 log 9 a. 27,-3 b. 28,-5 c. 25,-2 d. 26,-8 23. Evaluate: eloge8 a. 6 b. 8 c. 10 d. 4 24. Find the value of x if 8=log2x. a. 250 b. 245 c. 256 d. 259 25. Find the value of x if x = log381 a. 4 b. 5 c. 6 d. 7 26. The two legs of a triangle are 320 and 160 m each, respectively. The angle opposite the 160 m side is 28 deg. What is the third side? a. 227.5 m b. 232.3 m c. 250.1 m d. 240.9 m 27. What is the characteristics and mantissa of the common logarithm of 9.25? a. 0.5211 b. 0.6522 c. 0.7620 d. 0.9661 Answer Key (Handwritten) |
