...opposite one of them to find the other parts. EXAMPLE I.— Given В = 67° 22' 49", & = 45, с = 39. In any triangle the sides are proportional to the sines of the opposite angles, that is — c- • т > L- /^ Sin С с b : с :: Sin В : Sin С, or --:---- = ... ~ с. Sin В . . Sill С—...

...to obtain. Additional relations will then be derived from these. The Law of Sines. — In any plane triangle, the sides are proportional to the sines of the opposite angles. Let ABC be the triangle, CD one of its altitudes. Two cases arise, according as D falls within or without...

...perpendicular from A to a we may obtain, in a similar manner, sin C sin B bc sin A sin B sin C LAW OF SINES. In any triangle the sides are proportional to the sines of the opposite angles. When a side and two angles of a triangle are given we may find the other two sides by this law. PROBLEMS...

...С. (г) Equation (i) or (2) embodies what is known as the Law of Sines, which states that, — In any triangle the sides are proportional to the sines of the opposite angles. (b) Second proof. The Law of Sines may be proven in another way, which at the same time brings out...

...derived from the formulas growing out of the sine theorem and cosine theorem. 76. Sine theorem. — In any triangle the sides are proportional to the sines of the opposite angles. First proof. In Fig. 81, let ABC be any triangle, and let h be the perpendicular from B to AC. The...

...incidence, F'iAM = r= the angle of refraction, and Ri = AM = the radius of curvature of the lens. Since in any triangle the sides are proportional to the sines of the opposite angles, we have, in the triangle MAFiM: (i) i ART. 85] LENSES 117 and in the triangle MAF'\M sin r _ sinr_...

...(4) Therefore: a/sin A = b/sin B = c/sin C = 2R (5) Stated in words, the formula says: In any oblique triangle the sides are proportional to the sines of the opposite angles. (1) F1G. 119. — Derivation of the Law of Sines and the Law of Cosines. GEOMETRICALLY: Calling each...

...derived from the formulas growing out of the sine theorem and cosine theorem. 76. Sine theorem. — In any triangle the sides are proportional to the sines of the opposite angles. First proof. In Fig. 81, let ABC be any triangle, and let h be the perpendicular from В to AC. The...

...two as B and C, the third can be computed from the equation A = 3200 -(B + C). (2) That in any plane triangle the sides are proportional to the sines of the opposite angles, or in the triangle given, we may write the equation: SinB b Sin A a orb = aX Sin B^ Sin A (3) alsoc=aXSinC^-SinA...

...to obtain. Additional relations will then be derived from these. The Law of Sines. — In any plane triangle, the sides are proportional to the sines of the opposite angles. Let ABC be the triangle, CD one of its altitudes. Two cases arise, according as D falls within or without...