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Pre-Calculus Homework Solutions 201

Pre-Calculus Homework Solutions 201 - 31 32 33 34 35 CP is...

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CP is the hypotenuse of 30°-60°-90° triangle CPQ . CQ is the longer side and PQ is the shorter side. 2( PQ ) CP 2( PQ ) 4 3 PQ 2 3 3( PQ ) CQ 3(2 3) CQ 2(3) CQ 6 CQ Q is on CD 6 units to the right of C , so Q has coordinates (2 6, 5) (8, 5). P is 2 3 units above Q , so P has coordinates (8, 5 2 3). 31. ST is the shorter leg of a 30°-60°-90° triangle. SP 2( ST ) 6 3 2( ST ) 3 3 ST Then c 3 3. PT is a vertical line segment, so a c 3 3. PT 3( ST ) PT 3(3 3) PT 3 3 or 9 Then b 9. PQ SR , so PQ is a horizontal line segment. Thus d b 9. 32. 12 triangles 33. The smaller angle is rotated, so it is the 30° angle. 34. There are no gaps because when a 30° angle is rotated 12 times, it rotates 360°. 35. Sample answer: 36. 2 x 8 x 4 y 3( x ) y 3(4) or 4 3 y 2( z ) 4 3 2( z ) 4 2 3 z 4 2 3 2 2 z 4 2 6 z 2 6 z 37. BD 3( DH ) 8 3 3( DH ) 8 DH BH 2( DH ) BH 2(8) BH 16 38. 4 ¬ 2 a 2 ¬ a b ¬ 3( a ) b ¬ 2 3 b ¬ 2 c 2 3 ¬ 2 c 3 ¬ c d ¬ 3( c ) d ¬ 3( 3) d ¬ 3 d ¬ 2 e 3 ¬ 2 e 1.5 ¬ e f ¬ 3( e ) f ¬ 1.5 3 f ¬ 2 g 1.5 3 ¬ 2 g 0.75 3 ¬ g x ¬ 3( g ) x ¬ 3(0.75 3) x ¬ 0.75 3 2.25 39. The hexagon consists of six equilateral triangles. So, m UXY 60. WY bisects a 60° angle, so m XYW 30.
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