...(2) (3) The results obtained in (1), (2), and (3) enable us to state the law of sines as follows : The sides of a triangle are proportional to the sines of the opposite angles. Equations (1), (2), and (3) are often combined and written in the following manner : abo sin A sin...

...C (2) (3) The results obtained in (1), (2), and (3) enable us to state the law of sines as follows: The sides of a triangle are proportional to the sines of the opposite angles. Equations (1), (2), and (3) are often combined and written in the following manner: abc sin A sin B...

...depart from exact opposition. If, now, in Fig. 429 AF be drawn making an angle fa with AO, then, since the sides of a triangle are proportional to the sines of the opposite angles, OF _ sin fa ii cos (0i — fa) If, now, cos (fa - fa) be expanded and divided through by sin fa, we...

...^shT^shTfl' Remembering that the sine of an angle 6 is equal to the sine of its supplement, and that the sides of a triangle are proportional to the sines of the angles opposite, we have, from the triangles CPIand CP0, sin r = p'- r^ and sinj = pr^ sin 6 »' sin...

...•+ sin 2A + sin \A + 61114^ cA • , = tan — • cos A + cos 2 A + cos $A + cos $A 2 6. Prove that the sides of a triangle are proportional 'to the sines of the opposite angles. Show how to solve a triangle, given two angles and a side. 7. Express cos \A and sin \A in terms of...

...[10] and [11] of the Principles of Protective Geometry. The proof there given depends on the fact that the sides of a triangle are proportional to the sines of the opposite angles, and this theorem has been shown to be true for an imaginary triangle, provided that no side is a critical...

...order, and conversely. The exact relation between the sides and angles is given by the Law of sines. The sides of a triangle are proportional to the sines of the opposite angles. Symbolically, abc sin A ~ sin B ~ sin C Let ABC be any triangle, and draw the altitude CD = h. Then...

...small angle introduces a greater error in the computed distances than the same error in a larger angle. The sides of a triangle are proportional to the sines of the opposite angles, and in the measurement of these angles personal errors may be expected to occur. It is therefore desirable...

...derived likewise for sides a and c, and for b and c. abc sin A sin B sin C (12) That is, the three sides of a triangle are proportional to the sines of the opposite angles. [Memorize. ] What, if any, modifications are necessary when the triangle contains an obtuse angle will...

...— a sec0= cosec 0= — a vers 6= — c exsec 9= — c SOLUTION OF OBLIQUE TRIANGLES. Law of Sines. The sides of a triangle are proportional to the sines of the opposite angles. Law of Cosines. The square of the side of a triangle is equal to the sum of the squares of the other...