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Unformatted text preview: ) and C (b, 0).
From Theorem 10.3, we know that since the point B (x, y ) lies on a circle of radius c, the coordinates
of B are B (x, y ) = B (c cos(α), c sin(α)). (This would be true even if α were an obtuse or right angle
so although we have drawn the case when α is acute, the following computations hold for any angle
α drawn in standard position where 0 < α < 180◦ .) We note that the distance between the points
B and C is none other than the length of side a. Using the distance formula, Equation 1.1, we get
1 Here, ‘Side-Angle-Side’ means that we are given two sides and the ‘included’ angle - that is, the given angle is
adjacent to both of the given sides. 774 Applications of Trigonometry a=
a2 = (c cos(α) − b)2 + (c sin(α) − 0)2
(c cos(α) − b)2 + c2 sin2 (α) 2 a2 = (c cos(α) − b)2 + c2 sin2 (α)
a2 = c2 cos2 (α) − 2bc cos(α) + b2 + c2 sin2 (α)
a2 = c2 cos2 (α) + sin2 (α) + b2 − 2bc cos(α)
a2 = c2 (1) + b2 − 2bc cos(α) Since cos2 (α) + sin2 (α) = 1 a2 = c...
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