...— C)' 6 — c tani(B — C)' § 73. The square 'of any side of a triangle is equal to the sum of the squares of the other two sides, minus twice the product of those sides into the cosine of their included angle. FIG. 43. FIG 44. Through c in the triangle ABC...

...XXVIII. 68 1 In a triangle the square of a side opposite an acute angle is equivalent to the sum of the squares of the other two sides minus twice the product of one of these sides and the distance from the vertex of this acute angle to the foot of the perpendicular...

...circle : — (a). Any side is equal to twice the tangent from its middle point to the circle. (4). The square of any side is equal to the sum of the squares of the tangents from its extremities to the circle. 14. A square is described on the hypotheneuse...

...XXVIII. 68. In a triangle the square of a side opposite an acute angle is equivalent to the sum of the squares of the other two sides minus twice the product of one of these sides and the distance from the vertex of this acute angle to the foot of the perpendicular...

...required parts of the triangle from the altitude. CASE III. Given the three sides. THEOREM III. In a triangle the square of any side is equal to the sum of the squares of the other two sides minus twice the product of these two sides into the cosine of the angle...

...THEOREM VII. 259. In any triangle, the square on the side opposite an acute angle. equals the sum of the squares of the other two sides minus twice the product of one of those sides and the projection of the other upon that side. In the A ABC, let c be an acute...

...ca Since the result (80) may also be written a+b _ COt i Ü ХддЧ а — b tan b (A — В) 146. In any triangle the square of any side is equal to the sum of the squares of the other two sides, minus twice their product into the cosine of their included angle....

...Since A + В = 180° - С, we have Thus formula (48) may be put in the form a + b _ cot ^ С '51-. 116. In any triangle, the square of any side is equal to the sum of the squares of the other two sides, minus twice their product into the cosine of their included angle....

...(Art. 14). Thus formula (48) may be put in the form g + b _ cot £ C a — b~tau$(A — B)' (51) 116. In any triangle, the square of any side is equal to the sum of the squares of the other two sides, minus twice their product into the cosine of their included angle....

...tan~T(A — B)' with similar expressions for the other pairs of sides. (83) FIG. 21 bis. о 63. //( any triangle the square of any side is equal to the sum of the squares of the other two sides minus twice the product of these sides and the cosine of the included...