| Mathematics - 1836 - 798 pages
...It is obvious that the sides of the triangle will be r, + r3, r, -fr,, гз + r\ i but the area of a **triangle is equal to the square root of half the sum of the** sides multiplied by the several differences between this half sum and the sides. Now the half sum is... | |
| Benjamin Greenleaf - Geometry - 1862 - 532 pages
...preceding equation, we have cos ¿ A = 4lifZ^L) . (106) V be Similarly, (107) (108) ° That is, The cosine **of half of any angle of a plane triangle is equal...the square root of half the sum of the three sides,** into half the sum less the side opposite the angle, divided by the rectangle of the two adjacent sides.... | |
| Benjamin Greenleaf - Geometry - 1862 - 518 pages
...ts(sa) . (106) V ft c Similarly, / — rr (107) cos (7 = . A(s— iQ . (108) V ab That is, ?%e cosine **of half of any angle of a plane triangle is equal...the square root of half the sum of the three sides,** into half the sum less the side opposite the angle, divided by the rectangle of the two adjacent sides,... | |
| Benjamin Greenleaf - Geometry - 1861 - 638 pages
...4/li?^?) . (106) V bc Similarly, i : rr (107) ms j. <7— ./-"fr — c). (108) V aft That is, The cosine **of half of any angle of a plane triangle is equal to the square root of half the** mm of the three sides, into half the sum less the side opposite the angle, divided by the rectangle... | |
| Benjamin Greenleaf - Geometry - 1863 - 502 pages
...preceding equation, we have be Similarly, (106) ' (107) cos* tf= 4 *iz£. (108) That is, V ab The cosine **of half of any angle of a plane triangle is equal...the square root of half the sum of the three sides,** into half the sum less the side opposite the angle, divided by the rectangle of the two adjacent sides.... | |
| Benjamin Greenleaf - Geometry - 1863 - 504 pages
...— J?> . (106) V bc Similarly, cos j5=1/l('JzAJ, (107) cos A (7 = = V/^' (108) That is, The cosine **of half of any angle of a plane triangle is equal...the square root of half the sum of the three sides,** into half the sum less the side opposite the angle, divided by the rectangle of the two adjacent sides.... | |
| Benjamin Greenleaf - 1867 - 188 pages
...obtain sin tJS = JV— >*-">, (103) sin JC/ = -==. (104) That is, The sine of half of any angle in **a plane triangle is equal to the square root of half...half the sum less the other adjacent side, divided by** the rectangle of the two adjacent sides. 116. If 1 be added to both sides of (99), then, substituting... | |
| Lefébure de Fourcy (M., Louis Etienne) - Trigonometry - 1868 - 350 pages
...hence, sin í A = ч A V , be From which we form the following important rule, that the sine of half an **angle of a plane triangle is equal to the square root of half the sum of the three sides** minus one of the adjacent sides, multiplied by the half sum of the three sides minus the other adjacent... | |
| Benjamin Greenleaf - 1869 - 516 pages
...equation, we have (106) 6 c Similarly, (107) cos j. C = . /'~(,-0 . (108) V at That is, 7'As cosine **of half of any angle of a plane triangle is equal to** <Ae square root of half the sum of the three sides, into half the sum less the side opposite the angle,... | |
| Charles Davies - Geometry - 1872 - 464 pages
...e - 2 - = i» - c, and, - 3 - Substituting in ( 5 ), and reducing, we have, hence, sine cf half an **angle of a plane triangle, is equal to the square root of half the sum of the three sides,** minus one of the adjacent sides, into the half sum minus tht other adjacent side, divided by the rectangle... | |
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