...quantities we proceed as follows : — Suppose AB, BC, known, and the angle ABC. Then as the sum of the two sides Is to their difference, So is the tangent of half the sum of the two unknown angles To the tangent of half their difference. Half their difference thus found, added...

...two sides and the included angle, to find the rest. Proposition HI. may here be written as a rule. " As the sum of the given sides is to their difference, so is the tangent of half the sum of the opposite angles to the tangent of half their difference. And the half difference added to half the...

...the preceding section. Thus: take the given angle from 180°, the remainder will be the sum of the other two angles. Then say, — As the sum of the...difference ; So is the tangent of half the sum of _ the remaining angles, To the tangent of half their difference. Then, secondly, say, — As the cosine...

...this rule may be enunciated in general terms; thus, As the sum of two sides of a plane triangle'is to their difference, so is the tangent of half the sum of the angles opposite those sides to the tangent of half the difference of those angles. Let ABC (Fig. 47)...

...subtract them, this will give a + b and a — b/ then the sum of the sides is to their difference as the tangent of half the sum of the remaining angles to the tangent of half their difference. The half sum and half difference being added, gives the greater angle, which is always opposite the...

...required angle will be acute. When two sides and their included angle are given. — As the sum of any two sides is to their difference, So is the tangent of half the sum of their opposite angles, to the tangent of half their difference. Then the half difference of these angles,...

...BC DC 0 DC a 1. Sin В Or Sin A : sin B : : a : Ъ. (2) In any plane triangle, as the sum of any two sides is to their difference, so is the tangent of half the sum of the opposite angles, to the tangent of half their difference. From the preceding, we have, a^_ sin A Ъ...

...36" i sum 71° 50' 48" Here we will apply the following theorem in trigonometry. As the sum of two sides is to their difference, so is the tangent of half the sum of the angles at the base, to the tangent of half their difference. Let x= the half difference between D and...

...and the included angle are given. • RULE 4. To find the other side: — • as the sum of the two given sides is to their difference, so is the tangent of half the sum of their opposite angles to the tangent of half their difference — add this half difference to the half...

...opposite to the latter. 3. In any plane trianf/le, as the sum of the sides about the vertical angle is to their difference, so is the tangent of half the sum of the angles at the base to the tangent of half their difference. 4. In any plane triangle, as the cosine...