Two surveyors 180 meters apart on the same side of a river measure their respective angles to a point on the other side of the river and obtain 54 and 68 . How far from the point (line-of-sight distance) is each surveyor? Round your answers to the nearest 0.1 meter.
Could someone please explain how to solve this? Thanks.
2007-11-22 17:23:18 · 3 answers · asked by labelapark 6 in Science & Mathematics ➔ Mathematics
You need Trigonometry. The way I understand it, both guys are looking at the same point, they are on the same side of the river but separated (horizontally if you like) by 180 meters. So, you just get a triangle that has 180 meters on one side and those angles on each end of this 180 side.
2007-11-22 17:36:30 · answer #1 · answered by DaFro 2 · 2⤊ 0⤋
Triangle ABC is such that:-
A = 68°
B = 54°
C = 58°
BC = 180 m
Sine Rule
180 / sin 58° = b / sin 54°
b = 180 sin 54° / sin 58°
b = 171.7 m
171.7 / sin 54° = c / sin 68°
c = 171.7 sin 68° / sin 54°
c = 195.0 m
Distances are 171.7m and 195.0 m
2007-11-28 03:04:20 · answer #2 · answered by Como 7 · 1⤊ 1⤋
Let x and y be the two sides, and x > y
Use law of sine,
x/sin68 = 180/sin14
x = 689.9 m
y/sin54 = 180/sin14
y = 601.9 m
2007-11-22 18:27:25 · answer #3 · answered by sahsjing 7 · 1⤊ 1⤋