August 9, 2009
10 pts to 1st person to help me with trig story problem?
Roxanne asked:
I can't seem to visualize this picture. I'd appreciate it you label sides a, b, c and show work
thanks in advance!
I can't seem to visualize this picture. I'd appreciate it you label sides a, b, c and show work
thanks in advance!
A boat travels for 8 km in a straight line from the dock. It is then sighted from a lighthouse which is 6.5 km from the dock. The angle determined by the dock, the lighthouse (vertex) and the boat is 25°. How far is the boat from the lighthouse?
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cosine law
64=6.5^2+x^2-13xcos25
x=14.4
Consider a triangle ABC.
A: Boat, B: dock, C: lighthouse
AB = c = 8, BC = a = 6.5,
Sorry, it's really hard to draw a diagram on Y!A.
………………………..Boat (A) angle A = ?
………………………/BBB Lighthouse
……………………./….. ……
…………………../……. …….
…………………/……… …….. b = ?
..c.=.8.km…/………. ……….
………………/………… ………..
……………./———– ———- angle C = 25°
…….Dock……a.=.6.5.km…….Lighthouse
……..(B)…………………………….(C)
AB = 8 = c
BC = 6.5 = a
angle C = 25°
Use law of sines.
a / sinA = c / sin C
6.5 / sinA = 8 / sin(25°)
6.5 * sin(25°) = 8 * sinA
[6.5 * sin(25°)]/8 = sinA
sinA = 0.343377338
arcsin(0.343377338) = angle A
angle A = 0.350510527 radians = 20.0827739°
………………………..Boat (A) angle A = 20.0827739°
………………………/BBB Lighthouse
……………………./….. ……
…………………../……. …….
…………………/……… …….. b = ?
..c.=.8.km…/………. ……….
………………/………… ………..
……………./———– ———- angle C = 25°
…….Dock……a.=.6.5.km…….Lighthouse
……..(B)…………………………….(C)
We can figure out angle B now that we have angle A and angle C.
angle B = 180° - 20.0827739° - 25° = 134.917226°
………………………..Boat (A) angle A = 20.0827739°
………………………/BBB Lighthouse
……………………./….. ……
…………………../……. …….
…………………/……… …….. b = ?
..c.=.8.km…/………. ……….
………………/………… ………..
……………./———– ———- angle C = 25°
…….Dock……a.=.6.5.km…….Lighthouse
……..(B)…………………………….(C)
…….angle B = 134.917226°
Use law of sines.
b / sin B = c / sin C
b / sin(134.917226°) = 8 / sin(25°)
b = 8 / sin(25°) * sin(134.917226°)
b = 8 / 0.422618262 * 0.708127585
b = 13.4045809 km
………………………..Boat (A) angle A = 20.0827739°
………………………/BBB Lighthouse
……………………./….. ……
…………………../……. …….
…………………/……… …….. b = 13.4045809 km = ANSWER
..c.=.8.km…/………. ……….
………………/………… ………..
……………./———– ———- angle C = 25°
…….Dock……a.=.6.5.km…….Lighthouse
……..(B)…………………………….(C)
…….angle B = 134.917226°