Technical Mathematics, Sixth Edition

7.7. CHAPTER 7 REVIEW PROBLEMS

Write the sine, cosine, and tangent of each angle. Keep four decimal places.

1. 72.9° 0.9558, 0.2940, 3.2506

2. 35.226° 0.5768, 0.8169, 0.7061

3. 60.16° 0.8674, 0.4976, 1.7433

Find angle θ in decimal degrees, if

1. sin θ = 0.574 35.0°

2. cos θ = 0.824 34.5°

3. tan θ = 1.345 53.37°

Evaluate each expression. Give your answer in degrees.

1. arcsin 0.377 22.1°

2. cos⁻¹ 0.385s 67.4°

3. arctan 1.43 55.0°

Solve right triangle ABC.

1. a = 746 and A = 37.2° B = 52.8°; b = 983; c = 1230

2. b = 3.72 and A = 28.5° B = 61.5°; a = 2.02; c = 4.23

3. c = 45.9 and A = 61.4° B = 28.6°; b = 22.0; a = 40.3

4. Find the horizontal and vertical components of a vector that has a magnitude of 885 and makes an angle of with the horizontal. 356; 810

5. Find the magnitude of the resultant of two perpendicular vectors that have magnitudes of 54.8 and 39.4, and find the angle the resultant makes with the 54.8 vector. 67.5; 35.7°

6. A vector has horizontal and vertical components of 385 and 275. Find the magnitude and the direction of that vector. 473; 35.5°

7. A vertical pole on horizontal ground casts a shadow 13.5 m long when the angle of elevation of the sun is 15.4°. Find the height of the pole. 3.72 m

8. From a point 125 ft in front of a church, the angles of elevation of the top and base of its steeple are 22.5° and 19.6°, respectively. Find the height of the steeple. 7.27 ft

9. A circuit has a resistance of 125 Ω, an impedance of 256 Ω, an inductive reactance of 312 Ω, and a positive phase angle. Find the capacitive reactance and the phase ...