Chapter 14 Answers - BISD Moodle

((Chapter , Lesson second! They also explain that sound localizationvaries with frequency: low frequency soundsbend easily around a person’s head, whereas highfrequency sounds, whose wavelength is shortcompared with the size of the head, do not.Although the degree seems to have been usedto measure angles since angles were firstmeasured, the radian was invented in byJames Thomson, the brother of the physicist LordKelvin (William Thomson). Unlike the degree,based on the arbitrary division of a circle into parts, the radian is a natural unit of anglemeasure. In Trigonometric Delights (PrincetonUniversity Press, ), Eli Maor remarks that the“reason for using radians is that it simplifies manyformulas. For example, a circular arc of angularwidth θ (where θ is in radians) subtends an arclength given by s = rθ; but if θ is in degrees, thecorresponding formula is s = πr. Similarly,the area of a circular sector of angular width isA = θr for θ in radians and A = πr for θ indegrees. The use of radians rids these formulas ofπthe ‘unwanted’ factor .” Maor adds: “Evenmore important, the fact that a small angle andits sine are nearly equal numerically—the smallerthe angle, the better the approximation—holdstrue only if the angle is measured in radians. . . .•8. 15,700 m 2 . (From exercise 6.)Latitude.•9. About 6,220 mi. [ 2π(3,960) ≈ 6,220.]10. About 69 mi. ( ≈ 69.)11. About 1,380 mi. (20 ⋅ 69 = 1,380.)Driveway Design.•12. 2,009 ft 2 . (41 ⋅ 49 = 2,009.)•13. 887 ft 2 . [2( π(18) 2 ) + 8 ⋅ 18 + 13 ⋅ 18 ≈ 887.]14. 1,122 ft 2 . (2,009 – 887 = 1,122.)Two Sectors.15. πr 2 .•16. πr 2 . [ π(2r) 2 = πr 2 .]17. The yellow and blue areas are equal.Reuleaux Triangle.•18. 60°. (mAB = ∠C = 60°.)•19. πx. ( 2πx = πx.)It is this fact, expressed as= , that20. 3x.makes the radian measure so important incalculus.”Orange Slices.•1. A sector.•2. 45°. ( .)πr•3. πr. ( .)•4. πr 2 .Sonar Beams.•5. The length of AB in meters.6. The area of sector DAB in square meters.7. 105 m. (From exercise 5.)21. πx. (3 ⋅ πx = πx.)•22. x. (c = πd = πx; so d = x.)Sound Delay.•23. About 9 in. [About (7) + (7π) ≈ 9.]24. 13,200 in. (1,100 ⋅ 12 = 13,200.)•25. About 0.0007 second.( ≈ 0.0007 second.)The Radian.26. 2πr.•27. 360°.