SOLUTION: Jan is swimming in sea ocean when he spots two sharks. He tells you that his distance from shark 1 is 30 m, the distance between the sharks is 20 m and the angle at jan is 58 degre

Algebra ->  Trigonometry-basics -> SOLUTION: Jan is swimming in sea ocean when he spots two sharks. He tells you that his distance from shark 1 is 30 m, the distance between the sharks is 20 m and the angle at jan is 58 degre      Log On


   

Question 1146868: Jan is swimming in sea ocean when he spots two sharks. He tells you that his distance from shark 1 is 30 m, the distance between the sharks is 20 m and the angle at jan is 58 degrees. Show that jan must have made a mistake in measurement, since there is no such triangle.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
side opposite the angle is 20 meters.
angle is 58 degrees.
angle opposite the side that is 30 meters is x degrees.
using the law of sines, you get:
20 / sin(58) = 30 / sin(x)
cross multiply to get:
20 * sin(x) = 30 * sin(58)
solve for xin(x) to get:
sin(x) = 30 * sin(58) / 20 = 1.27
sine can't be greater than 1, so the triangle is not possible, given those measurements.
here's my diagram of what i think is the situation.

$$$

BAC (angle A) is angle between the sharks at point B and C.
B is the location of the first shark.
C is the location of the second shark.
AB is opposite angle C.
BC is opposite angle A.
law of sines is used.
BC / sine (A) = AB / sine (C)
BC = 20
AB = 30
sine (A) = sine (58)
that gets you:
20 / sine (58) = 30 / sine (C)
solve for sine (C) as shown in he diagram.