Wes saw fireworks at 28 degrees; Abby (who was standing 20 m away from him) saw the same fireworks at a 40 degree angle. Where was Abby standing?
2 answers
Wes saw fireworks at 28 degrees; Abby (who was standing 20 m away from him) saw the same fireworks at a 40 degree angle. Where was Abby standing?
H is at height of explosion above ground
B is point below explosion on ground
first find distance AH
other angle at A = angle HAW = 180 - 40 = 140
so third angle in that triangle WHA = 180-140-28=12 degrees
so
sin 12/20 = sin 28/AH
AH = 20 sin 28/sin 12 = 20 * .426 / .187 = 45.6
that is thehypotenuse of triangle ABH
so
sin 40 = BH / 45.6
and
cos 40 = AB / 45.6
B is point below explosion on ground
first find distance AH
other angle at A = angle HAW = 180 - 40 = 140
so third angle in that triangle WHA = 180-140-28=12 degrees
so
sin 12/20 = sin 28/AH
AH = 20 sin 28/sin 12 = 20 * .426 / .187 = 45.6
that is thehypotenuse of triangle ABH
so
sin 40 = BH / 45.6
and
cos 40 = AB / 45.6
1 answer