two people start walking from the same point. Person A walks due east for 3.5 km and the person B walks in the direction 123 degrees until they are due south of person A. How far did the second person walk?

Question

two people start walking from the same point. Person A walks due east for 3.5 km and the person B walks in the direction 123 degrees until they are due south of person A. How far did the second person walk?

Answer 1

Dcos123=3.5

solve for D

Answer 2

watch out for the difference between bearings and polar directions.

Answer 3

To find out how far the second person walked, we can split their movement into two components: the east-west component and the north-south component.

First, let's find the east-west component. Person A walks due east for 3.5 km, so the second person needs to reach the same east coordinate as person A. Since the second person starts from the same point but walks at an angle of 123 degrees, we can use trigonometry to find the east-west component.

The east-west component is calculated by multiplying the total distance traveled (unknown) by the cosine of the angle. In this case, the angle is 123 degrees. The formula is: east-west component = distance × cos(angle)

Next, let's find the north-south component. Since the second person is trying to get due south of person A, we need to find the distance traveled directly south. This distance can be calculated using trigonometry as well.

The north-south component is calculated by multiplying the total distance traveled (unknown) by the sine of the angle. In this case, the angle is 123 degrees. The formula is: north-south component = distance × sin(angle)

Now, we can use the Pythagorean theorem to find the total distance traveled by the second person. The Pythagorean theorem states that the square of the hypotenuse (the total distance) is equal to the sum of the squares of the other two sides (east-west and north-south components). The formula is: total distance = √(east-west component^2 + north-south component^2)

Let's plug in the values and calculate:

For the east-west component:
east-west component = distance × cos(angle)
east-west component = distance × cos(123 degrees)

For the north-south component:
north-south component = distance × sin(angle)
north-south component = distance × sin(123 degrees)

Now, we can use the Pythagorean theorem:
total distance = √(east-west component^2 + north-south component^2)

By calculating the above equations, we can find the distance traveled by the second person.