Two Men, P And Q Set Off From A Base Camp R Prospectively For Oil.P Moves 20km On A Bearing Of 205 And Q Moves 15km On A Bearing Of 060.What Is The Distance Of P From Q

you don't move on a bearing. You move on a heading. You observe on a bearing.

Starting from R at (0,0),
P moves to (-20/√2,-20/√2)
Q moves to (15√3/2,15/2)

now just find the distance between those points.

Or, use the law of cosines. The angle between their headings is 165°, so their distance apart is

d^2 = 20^2 + 15^2 - 2*20*15 cos165°

pls solve it

To find the distance between two points, we can use the Pythagorean theorem.

Let's label the starting point as "R."

P moves 20km on a bearing of 205°. This means P moves 20km in the direction of 205° from R.

Q moves 15km on a bearing of 060°. This means Q moves 15km in the direction of 060° from R.

To find the distance between P and Q, we need to find the horizontal and vertical components of the distance traveled by P and Q.

The horizontal component of the distance traveled by P is given by 20 * cos(205°), and the vertical component is given by 20 * sin(205°).

Similarly, the horizontal component of the distance traveled by Q is given by 15 * cos(60°), and the vertical component is given by 15 * sin(60°).

Let's calculate these values:

Horizontal component of P = 20 * cos(205°) = -8.09 km (rounded to two decimal places)
Vertical component of P = 20 * sin(205°) = -15.94 km (rounded to two decimal places)
Horizontal component of Q = 15 * cos(60°) = 7.50 km (rounded to two decimal places)
Vertical component of Q = 15 * sin(60°) = 12.99 km (rounded to two decimal places)

Now, we can calculate the distance between P and Q using the Pythagorean theorem:

Distance = √( (Horizontal component of P - Horizontal component of Q)^2 + (Vertical component of P - Vertical component of Q)^2 )

Distance = √( (-8.09 - 7.50)^2 + (-15.94 - 12.99)^2 )

Distance = √( (-15.59)^2 + (-28.93)^2 )

Distance = √( 243.08 + 836.59 )

Distance = √(1079.67)

Distance ≈ 32.87 km (rounded to two decimal places)

Therefore, the distance between P and Q is approximately 32.87 kilometers.

To find the distance between Point P and Point Q, we can use the Pythagorean theorem. This theorem states that 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, let's assume that the starting point R is our origin, so its coordinates are (0, 0).

Now, we need to determine the coordinates of Point P. P moves 20 km on a bearing of 205 degrees. A bearing is a clockwise angle measured from the north direction.

To find the x-coordinate of P, we can use trigonometry. Since the bearing is measured from the north direction, and the angle is measured clockwise, we need to subtract the angle from 360 to get the angle measured counterclockwise from the positive x-axis direction.

The x-coordinate of P can be calculated as follows:
x-coordinate of P = distance * cos(angle)
= 20 km * cos(360 - 205)
= 20 km * cos(155)

Similarly, to find the y-coordinate of P, we can use trigonometry. The y-coordinate of P can be calculated as follows:
y-coordinate of P = distance * sin(angle)
= 20 km * sin(360 - 205)
= 20 km * sin(155)

Now, let's find the coordinates of P:
Coordinates of P = (x-coordinate of P, y-coordinate of P)

Next, we need to determine the coordinates of Point Q. Q moves 15 km on a bearing of 060 degrees.

The x-coordinate of Q can be calculated as follows:
x-coordinate of Q = distance * cos(angle)
= 15 km * cos(360 - 60)
= 15 km * cos(300)

The y-coordinate of Q can be calculated as follows:
y-coordinate of Q = distance * sin(angle)
= 15 km * sin(360 - 60)
= 15 km * sin(300)

Now, let's find the coordinates of Q:
Coordinates of Q = (x-coordinate of Q, y-coordinate of Q)

Finally, we can use the distance formula to find the distance between P and Q:
Distance between P and Q = sqrt((x-coordinate of P - x-coordinate of Q)^2 + (y-coordinate of P - y-coordinate of Q)^2)