Construction Michelle and Rick Bonneau are building a patio along the back wall of their home. The patio is designed in such a way that its outer border is an arc of a circle with center at point A and radius r, as shown in the aerial view in the accompanying figure. The angle is between radii AC and AD, point B is the midpoint of CD (which is of length l ), and BE (which is of length w) is perpendicular to CD.
(a) Express sin in terms of r and l.
(b) Express r in terms of sin and l.
(c) Use your answer to part (b) to find the value of r if l = 50, cos ?? = -0.4, and ?? is in the second quadrant.
(d) Express cos in terms of r and w.
(e) Express r in terms of cos and w.
(f ) Use your answer to part (e) to find the value of r if w = 15, tan ?? = 12, and ?? is in the first quadrant.
(g) What is the value of ?? (in radians) if l = 40 and the distance from point A to point B is 20?
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