From your window you can see a high-rise building several blocks away.You check the map and see that the building is 560 m away from you in a straight line, in a direction 30° south of east.However, the roads are all east-west and north-south.If you want to walk from your house to the building, how far in each direction do you have to walk?
A)480 m east and 280 m south
B)280 m east and 480 m south
C)280 m east and 280 m south
D)480 m east and 50 m south
E)cannot be determined without looking at the streets on the map

Question

Quizplus · Accepted Answer

To get to the building, we need to break down the 560m distance into its eastward and southward components. We know that the building is 30° south of east, which means that the angle between the straight-line distance and the eastward direction is 30°. Using trigonometry, we can find the eastward and southward components as follows:

Eastward distance = 560m * cos(30°) = 485m (rounded to the nearest whole number)
Southward distance = 560m * sin(30°) = 280m (rounded to the nearest whole number)

Since the roads are all east-west and north-south, we need to walk 485m east and 280m south to reach the building. Therefore, the best choice is A) 480m east and 280m south.

From Your Window You Can See a High-Rise Building Several