Question

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13) Two friends are standing on shore 500 feet apart at points F and G and each measures the angle to a sailboat at point H at the same time, forming triangle FGH. AngleF is 63' and angle G is 56". Find the distance from the friend at point F to the sailboat. Round the answer to the nearest tenth. Use a polar coordinate system to plot and label the given points. (+4) 14) A C (-3,90") B (4.-135) D(5,60") 15) Give another representation in polar form of the point D(5,60") above. (-2) 6

Answer 1

13 IN AFGH, we have KE = 630 KG = 56° FG = 5ooft 4630 568 G F Then LH = 100°- (2FtLG) LH= 180° - (63° +569) LAE 61° sooft pesing Law of sines Sin Es sin GL HF شیک - GIH FG love need to find FH. then Sis G. Sinh FH FG sin 56° FH = sin 610 500 FH= 500 Sin (56) Sin 610 FH= 500 (0.829031 513) 0.0746 19707 - 413.941741 EH = 414.518187 0.074619707 FHz 413,9 ft

4, -135 I | A) (-3, 3} T-3,3y) ( 13, 31) (4-135) c) (-3,90) D) (5, bo) II (2,90) (5,609) 390)

15 we have point D(5, 60) (5,60°)= (5, 60° + 366) =(5, 420°) (5,60°) (5,420°) 42.00