Since the triangle NMB is right-angled, we have BN2 = NM2 + BM2 = 23361 + 1600 = 3936). Again, since the triangle NBE, or its equal NBF, is right-angled at B, we have NE2= NF2BN2+ BE2 = 3936 +1210016036). And NE NF = NG=ND=√160363=126.63, nearly, for the number of feet from the point N to the top of each tree. END OF PART L TRIGONOMETRY. CHAPTER I. FIRST PRINCIPLES OF PLANE TRIGONOMETRY. § 1. TRIGONOMETRY is that science which investigates the relations of the sides and angles of triangles. When confined to plane triangles, it is called Plane Trigonometry. Definition of an Angle. 82. When two straight lines, AB, AC, meet each other, the opening between these lines is called an angle. This angle or opening, which is read BAC or CAB, or simply the angle at A, does not depend upon the lengths of these lines, but only upon the difference of their directions. C6 angle CAC; and the same for other arcs and their corresponding angles. Hence, the arcs thus described may be taken as measures of their corresponding angles. § 4. When the line AC, has reached the position AC, so that the arc CC, is a quadrant, or one-fourth of the entire cir |