Question

Points A and Bare separated by a lake. To find the distance between them, a surveyor locates a point Con land such than ZA = 51.6°. Find the distance across the lake from A to B. B 480 meters 57.6° 387 meters -O NOTE: The picture is NOT drawn to scale. Round all answers to 3 decimal places. Distance meters

Answer 1

Formula Used: law of sines! A c b Note: side a is opposite to angle a similarly side b is opposite to LB side c is opposite to angle c & C a B in A ABC law of sines state that sina sinB sinc - с. b

B Answer: a=480 We have a = 480 meters b = 387 meters ZA = 51.6° 51.69 C b=387 А use the law of sines to find the missing angle B so, by law of sines sinA SinB b sin B sinis 1.6) 480 387 sinB 387 X sin (51.6) 480 387 X 0.783693 11 [ use 480 calculator to calculate sin (51.6°) 303.289 480 sinB 0.632 LB sin-!(0.632) 39.1989 LB =

Now, LAT LB the = 180° [ sum of interior angle of a triangle is always 18.00 ] 51.60 + 39.198° + C = 180 90.798° + cc - 180° LC-180° - 90.798° LC = 89.202° Now , to find missing 9 use the law of Co Sines side AB =C so by law of sines sin A sinc C sin (89.2020 sin (51,6°) 480 с. cx sin ( 51.60) = 480 X sin (89.2020) 480 X sin (89.202) => c = sin (51.6°) 480 X 0.9999030 0.783693 479.953 0.783693 C 612.425
the distance between A and B is :612.425 meters