Ricardo and Jane are standing under a tree in the middle of a pasture. An argument ensues, and they walk away in different directions. Ricardo walks 28.0 in a direction 60.0 west of north. Jane walks 10.0 in a direction 30.0 south of west. They then stop and turn to face each other

**What is the distance between them?
**In what direction should Ricardo walk to go directly toward Jane?

R is right but i want the right answer for the second part ( ricardo needs .... to walk) PLEASE HELP ME

use law of cosines to get the distance:

d^2 = 28^2 + 10^2 - 2(10)(28)cos60°
= 604
d = 24.58

Let the triangle be TRJ, where R is where Ricardo ended up, T is the tree, and J is where Jane ended up.

To get the angle R, use the law of sines
sinR/10 = sin60°/24.58
sinR = .3523
R = 20.62°

Ricardo needs to walk E 50.62° S

If you have a hard time visualizing that, draw the diagram.

it's showing that my answer is wrong.. thanks anyway

i need help pls! the due time is after 12 hours

To find the distance between Ricardo and Jane, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

First, we need to find the horizontal and vertical components of the distance walked by each person. We can do this using trigonometric functions.

For Ricardo:
Distance walked in the north direction = 28.0 * sin(60) = 24.2 units (rounded to one decimal place)
Distance walked in the west direction = 28.0 * cos(60) = 14.0 units

For Jane:
Distance walked in the west direction = 10.0 * cos(30) = 8.7 units (rounded to one decimal place)
Distance walked in the south direction = 10.0 * sin(30) = 5.0 units

Now, let's find the difference between their horizontal and vertical components:
Horizontal distance = 14.0 - 8.7 = 5.3 units (rounded to one decimal place)
Vertical distance = 24.2 + 5.0 = 29.2 units (rounded to one decimal place)

Using the Pythagorean theorem:
Distance between Ricardo and Jane = sqrt((horizontal distance)^2 + (vertical distance)^2)
Distance between Ricardo and Jane = sqrt((5.3)^2 + (29.2)^2)
Distance between Ricardo and Jane ≈ 29.8 units (rounded to one decimal place)

To find the direction Ricardo should walk to go directly toward Jane, we can use trigonometry again. We need to find the angle between the line connecting Ricardo and Jane (the hypotenuse) and the north direction.

Angle = atan(vertical distance / horizontal distance)
Angle = atan(29.2 / 5.3)
Angle ≈ 80.3 degrees (rounded to one decimal place)

However, since Ricardo is already facing in the northwest direction (60 degrees west of north), he needs to turn towards the southeast to walk directly towards Jane.

Therefore, Ricardo should walk in a direction 60 + 80.3 = 140.3 degrees west of north to go directly toward Jane.