Two men P and Q set up from a base town R prospecting for oil. P moves 20km on a bearing 205 degree and Q moves 15km on a bearing 060 degree .calculate
(1) distance of q from P
(2) the bearing of Q from P
you have the data to make a sketch. Now, you have two sides, and the included angle. Now connect q and P, and you have a triangle.
a) use law of cosines to solve.
b) I would use law of sines to solve.
1. d = 20km[205o] - 15km[60o].
X = 20*sin205 - 15*sin60 = -21.44 km.
Y = 20*Cos205 - 15*Cos60 = -25.63 km.
d = sqrt(X^2 + Y^2) =
2. TanA = X/Y, A = 39.9o W. of S. = 219.9o CW or bearing.
To calculate the distance and bearing between points P and Q, we can use trigonometry and some basic principles of geometry.
Firstly, let's represent the movements of P and Q on a coordinate plane. Assume that the base town R is at the origin (0, 0).
P moves 20km on a bearing of 205 degrees. We can find P's final position by considering the horizontal and vertical components of this movement.
Horizontal component of P's movement = 20km * cos(205 degrees)
Vertical component of P's movement = 20km * sin(205 degrees)
Now, let's calculate these values:
Horizontal component of P's movement = 20km * cos(205 degrees) ≈ -17.29 km (rounded to two decimal places)
Vertical component of P's movement = 20km * sin(205 degrees) ≈ 11.90 km (rounded to two decimal places)
Therefore, P's final position is approximately (-17.29 km, 11.90 km).
Q moves 15km on a bearing of 060 degrees. Similar to P, we can find Q's final position by considering the horizontal and vertical components of this movement.
Horizontal component of Q's movement = 15km * cos(60 degrees)
Vertical component of Q's movement = 15km * sin(60 degrees)
Now, let's calculate these values:
Horizontal component of Q's movement = 15km * cos(60 degrees) ≈ 7.50 km (rounded to two decimal places)
Vertical component of Q's movement = 15km * sin(60 degrees) ≈ 12.99 km (rounded to two decimal places)
Therefore, Q's final position is approximately (7.50 km, 12.99 km).
Now, let's calculate the distance between P and Q:
Distance between P and Q = √((horizontal component of P's movement - horizontal component of Q's movement)^2 + (vertical component of P's movement - vertical component of Q's movement)^2)
Substituting the values we calculated before:
Distance between P and Q = √((-17.29 km - 7.50 km)^2 + (11.90 km - 12.99 km)^2)
= √((-24.79 km)^2 + (-1.09 km)^2)
= √(613.84 km^2 + 1.19 km^2)
≈ √615.03 km^2
≈ 24.79 km
Therefore, the distance between P and Q is approximately 24.79 km.
To calculate the bearing of Q from P, we can use the direction angles (also known as azimuth angles) between the base town R and points P and Q.
Bearing of Q from P = arctan((vertical component of Q's movement - vertical component of P's movement) / (horizontal component of Q's movement - horizontal component of P's movement))
Substituting the values we calculated before:
Bearing of Q from P = arctan((12.99 km - 11.90 km) / (7.50 km - (-17.29 km)))
= arctan(1.09 km / 24.79 km)
≈ arctan(0.044) (rounded to three decimal places)
≈ 2.512 radians (rounded to three decimal places)
≈ 144.019 degrees (rounded to three decimal places)
Therefore, the bearing of Q from P is approximately 144.019 degrees.
To summarize:
(1) The distance of Q from P is approximately 24.79 km.
(2) The bearing of Q from P is approximately 144.019 degrees.