A ship travels 58 km on a bearing of 37 degrees, and then travels on a bearing of 127 degrees for 128 km, find the distance of the end of the trip from the starting point, to the nearest kilometer
A) 186km
B) 141 km
C) 35 km
D) 46 km
A) 186km
B) 141 km
C) 35 km
D) 46 km
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The answer is B. I made a diagram for you here:
http://i.imgur.com/rRGRf.jpg
Bearing is measured clockwise from true north. You know the 37° and the 127° angles from the problem. You know that the smaller component of the biggest angle is also 37° because a transverse line going through two parallel lines will create two identical angles. The larger component of the biggest angle is 53° because it is a complementary angle to the given 127° angle. 37° + 53° = 90°. Because you know that you have a right triangle, you can use the Pythagorean theorem to solve the problem. 58^2+128^2=140.5
Answer is 140.5, rounded to 141km, which is B.
http://i.imgur.com/rRGRf.jpg
Bearing is measured clockwise from true north. You know the 37° and the 127° angles from the problem. You know that the smaller component of the biggest angle is also 37° because a transverse line going through two parallel lines will create two identical angles. The larger component of the biggest angle is 53° because it is a complementary angle to the given 127° angle. 37° + 53° = 90°. Because you know that you have a right triangle, you can use the Pythagorean theorem to solve the problem. 58^2+128^2=140.5
Answer is 140.5, rounded to 141km, which is B.