Carolyn rides her bike

πœƒ = 39.3Β°
south of west for
d = 4.60 miles
What is the distance she would have to ride due south and due west to reach the same location?

=miles south
=miles west

draw a diagram

x (west) = d cosπœƒ
y (south) = d sinπœƒ

Thank you

To find the distance Carolyn would have to ride due south and due west to reach the same location, we can use trigonometry.

First, let's find the distance she rides due south (y-direction) and due west (x-direction) separately using the given angle and distance.

For the distance due south (y-direction), we can use the formula:

y = d * sin(πœƒ)

where:
- y is the distance due south
- d is the given distance (4.60 miles in this case)
- πœƒ is the given angle (39.3Β° in this case)

Plugging in the values, we have:

y = 4.60 * sin(39.3Β°)
y = 4.60 * 0.629
y β‰ˆ 2.895 miles (rounded to three decimal places)

For the distance due west (x-direction), we can use the formula:

x = d * cos(πœƒ)

where:
- x is the distance due west
- d is the given distance (4.60 miles in this case)
- πœƒ is the given angle (39.3Β° in this case)

Plugging in the values, we have:

x = 4.60 * cos(39.3Β°)
x = 4.60 * 0.777
x β‰ˆ 3.580 miles (rounded to three decimal places)

Therefore, Carolyn would have to ride approximately 2.895 miles due south and 3.580 miles due west to reach the same location.