...sides and third angle required in the proposed triangle. It is easily seen, also, that all the formulae above given for this case might have been obtained...considerations. 84. CASE III. Given two sides and an Fig.e. angle opposite one of them; or a. b, and A. Fig. 9. First Solution, in which each required part...

...sides and third angle required in the proposed triangle. It is easily seen, also, that all the formulae above given for this case might have been obtained by these considerations. 84. CASE III. Q.iven two sides and an angle opposite one of them ; or a, b, and A. Fig. 9. First Solution, in which...

...the other given side. 89. CASE IV. Given two angles and a side opposite one of them, or A, B and b. (Fig. 9). First Solution, in which each required part is deduced directly from the fundamental formulae. To find c. We have, by (10), sin с cot 5 — cos e cos A = sin A cot В...

...sides and third angle required in the proposed triangle. It is easily seen, also, that all the formulae above given for this case might have been obtained...required part is deduced directly from fundamental formula independently of the other two parts. To find c. We have, by (4),* cos с cos i + sin с sin...

...sides and third angle required in the proposed triangle. It is easily seen, also, that all the formula; above given for this case might have been obtained...Solution, in which each required part is deduced directly fron> fundamental formulx independently of the other two parts. To finde. We have, by (4),* cos c cos...

...Д. sin Ue • cot a = cot с sec Bc cos Д, sin b = sin В sin с esc О = sin 5 sin a esc A 194i CASE III. Given two sides and an angle opposite, one of them, a, b, and A. Two triangles, both, possible when sin a ^> sin 6 sin A, both impossible when sin a <...

...given A = 74° 9' 4", b = 246.388, c = 902.188. Find .ft, C, and a. 10. Given, two- sides of a triangle and an angle opposite one of them, or a, b, and A. What are the conditions that there shall be two solutions ? Give three cases when there will be one...

...ten figures, ch could not be done by the ordinary methods without ten-figure tables. 132. CASE II. Given two sides and an angle opposite one of them, or a, i and A. To find B. To find the angle opposite the other given side, we apply Art. 117, and state the...

...only six distinct cases, as follows : CASE I. Given the three sides. CASE II. Given the three angles. CASE III. Given two sides and an angle opposite one of them. CASE IV. Given two angles and a side opposite one of them. CASE V. Given two sides and the included...

...only six distinct cases, as follows : CASE I. Given the three sides. CASE II. Given the three angles. CASE III. Given two sides and an angle opposite one of them. CASE IV. Given two angles and a side opposite one of them. § 26. Cases I. and II. can be solved by...