...Г23] еm A smB sin С LJ Observe that if С = 90°, sin С = 1 and [23] gives a/c = sin A and &/c = sin B, which are the known relations in the right.angled...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 their...

...[23] s1n A s1n В s1n С LJ Observe that if С = 90°, sin С = 1 and [23] gives a/c = sin A and b/c = sin B, which are the known relations in the right-angled...diameter of the circle circumscribed about the triangle ABС. Law of cosines. In any triangle the square of any side is equal to the sum of the squares of...

...constructions. 2. In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides, minus twice the product of one of these sides and the projection of the other side upon it. 3. The areas of two similar triangles...

...memory. 19. The Cosine Principle. — fn any triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice the product of these two sides and the cosine ot their included angle. That is (Fig. 6), a' = b' + c' - 2 bc cos A b' = a' + c' —...

...memory. 19. The Cosine Principle. — In any triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice the product of these two sides and the cosine of their included angle. That is (Fig. 6), a' = f + c' - 2 bc cos A 6' = a' + c' - 2...

...in like manner, or can be obtained from (3) by symmetry : These formulas can be expressed in words : In 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 two sides multiplied by the cosine...

...346. THEOREM. In any triangle the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides minus twice the product of one of these two sides and the projection of the other side upon that one. Given: (?). To Prove: c2=(?)....

...calculated by the simple formulas of trigonometry. The most important formula used is the one stating that "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."...

...346. THEOREM. In any triangle the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides minus twice the product of one of these two sides and the projection of the other side upon that one. Given: (?). To Prove: c2=(?)....

..., b2 = c? + a>-2cacosB, i? = a2 + 62 - 2 ab cos C. (3') These formulas can be expressed in words : In 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 two sides multiplied by the cosine...