The following problem involves directions in the form of bearing, which we defin
ID: 2905734 • Letter: T
Question
The following problem involves directions in the form of bearing, which we defined in this section. Remember that bearing is always measured from a north-south line.
A.) A man wandering in the desert walks 2.4 miles in the direction S 34° W. He then turns 90° and walks 3.2 miles in the direction N 56° W. At that time, how far is he from his starting point, and what is his bearing from his starting point? (Round your answers to the nearest whole number.)
B.)Two planes take off at the same time from an airport. The first plane is flying at 190 miles per hour on a bearing of S 45.0° E. The second plane is flying in the direction S 45.0°W at 295 miles per hour. If there are no wind currents blowing, how far apart are they after 4 hours? (Round your answer to two decimal places.)
mi
What is the bearing of the second plane from the first after 4 hours? (Round your answer to one decimal place.)
S ° W
Explanation / Answer
a) since it forms a right angled triangle
distance travelled =sqrt (3.2^2 + 2.4^2) = 4 miles
the bearing from starting point
sin^-1 ( 3.2/4) = 53.13
bearing = 53.13+ 34 = 87 degrees
B ) distance = speed / time
for plane 1
distance travelled = 190 / 4 = 47.5 miles to south east
plane 2
distance = 295/4 = 73.75 miles to south west
for a right angled triangle whose two sides are (47.5) and (73.75)
distance between two planes = sqrt (47.5^2 + 73.75^2 )
distance between two planes = 87.72 miles
bearing = theta = tan^-1 ( 47.5/ 73.75) = 32.78 degrees
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