Two men P and Q set out prospecting for oil from a base camp R. P moves 20km on a bearing of 205 degree and Q moves 30km on a bearing of 060. Calculate The distance from Q to P
determine the angle between the paths (205--60)=145
apply the law of Cosines:
c^2=a^2+b^2-2abCosC
All angles are measured CW from +y-axis.
d = 20km[205o] - 30km[60o].
X = 20*sin205 - 30*sin60 = -34.43 km.
Y = 20*Cos205 - 30*Cos60 = -33.13 km.
d = sqrt(X^2 + Y^2).
To calculate the distance from Q to P, we can use the Pythagorean theorem. First, let's find the horizontal and vertical distances traveled by P and Q.
For P:
- Horizontal Distance = 20 km * cos(205 degrees)
- Vertical Distance = 20 km * sin(205 degrees)
For Q:
- Horizontal Distance = 30 km * cos(60 degrees)
- Vertical Distance = 30 km * sin(60 degrees)
Now, we can calculate the distance between P and Q using the Pythagorean theorem:
Distance = √((Horizontal Distance of Q - Horizontal Distance of P)^2 + (Vertical Distance of Q - Vertical Distance of P)^2)
To calculate the distance from point Q to point P, we can use the Pythagorean theorem.
First, let's visualize the situation. Imagine a coordinate system where the base camp R is the origin (0,0) and the bearings represent the directions in which P and Q moved.
P moved 20km on a bearing of 205 degrees. We can break this movement into horizontal and vertical components. To find the horizontal component, we need to find the cosine of the angle.
Horizontal component of P's movement = 20 km * cos(205 degrees)
To find the vertical component, we need to find the sine of the angle.
Vertical component of P's movement = 20 km * sin(205 degrees)
Similarly, Q moved 30km on a bearing of 060 degrees. We can again break this movement into horizontal and vertical components.
Horizontal component of Q's movement = 30 km * cos(60 degrees)
Vertical component of Q's movement = 30 km * sin(60 degrees)
Now, we can calculate the distance between Q and P using the Pythagorean theorem:
Distance = square root ((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)