A boat leaves the entrance of a harbor and travels 64 miles on a bearing of N 31 degrees E. How many miles north and how many miles east from the harbor has the boat traveled?
Thanks in advance
Thanks in advance
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Hi :
to solve this Draw a picture of a right triangle a put 64 for h
to find How for north the boat is from the harbor use
o = h*sine(thea)
o = 64* sine (31)
o = 64 *0.51503807491005421008163193639814
o= 32.962436794243469445224443929481 or 33 miles north (round to the nearest mile)
to find How far east the boat is from the entrance of a harbor use
a = h*cos( thea)
a = 64 * cos(31)
a = 64 * 0.85716730070211228746521798014476
a = 54.858707244935186397773950729265 or 55 miles ( rounded to the nearest mile) east of the entrance of a harbor
proof or check
o^2 + a^2 = h^2
since h = 64 and 64 ^2 = 4096, and o = 32.962436794243469445224443929481, a = 54.858707244935186397773950729265 So
32.962436794243469445224443929481^2 + 54.858707244935186397773950729265^2 = 4096
1086.5222394144956908350212337094 + 3009.4777605855043091649787662906 = 4096
4096 = 4096
sqrt(4096) = sqrt(4096)
64 = 64
it check and equals
to solve this Draw a picture of a right triangle a put 64 for h
to find How for north the boat is from the harbor use
o = h*sine(thea)
o = 64* sine (31)
o = 64 *0.51503807491005421008163193639814
o= 32.962436794243469445224443929481 or 33 miles north (round to the nearest mile)
to find How far east the boat is from the entrance of a harbor use
a = h*cos( thea)
a = 64 * cos(31)
a = 64 * 0.85716730070211228746521798014476
a = 54.858707244935186397773950729265 or 55 miles ( rounded to the nearest mile) east of the entrance of a harbor
proof or check
o^2 + a^2 = h^2
since h = 64 and 64 ^2 = 4096, and o = 32.962436794243469445224443929481, a = 54.858707244935186397773950729265 So
32.962436794243469445224443929481^2 + 54.858707244935186397773950729265^2 = 4096
1086.5222394144956908350212337094 + 3009.4777605855043091649787662906 = 4096
4096 = 4096
sqrt(4096) = sqrt(4096)
64 = 64
it check and equals
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since the bearing=31º, theta=90-31=59º
draw x0y
y=north, x=east
from north draw towards east 31ºangle, draw a line from irigin (0,0) out on this line representing 64miles, with the arrow poiting out.
the righ triangle is formed by this line and the axises
cosθ=x/64
sinθ=y/64[trig basic identities]
x=64cosθ=64cos59=32.96=33 miles east
y=64sinθ=64sin59=54.86=55 miles north
draw x0y
y=north, x=east
from north draw towards east 31ºangle, draw a line from irigin (0,0) out on this line representing 64miles, with the arrow poiting out.
the righ triangle is formed by this line and the axises
cosθ=x/64
sinθ=y/64[trig basic identities]
x=64cosθ=64cos59=32.96=33 miles east
y=64sinθ=64sin59=54.86=55 miles north
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Ok, go ahead.