A man walks 5km south and then 3km in the direction 60degrees west of south.His distance from the starting point is?
Y is it 120 degrees
Law of Cosines:
distance^2=5^2+3^2-2*5*3*cos120deg.
wrong answer
I'm confused on the working
To find the distance from the starting point, we can break down the man's movement into two components: one in the north-south direction and the other in the east-west direction.
Let's first consider the movement in the north-south direction. The man walks 5 km south, which means he is moving directly opposite to the north direction. So, his north-south component of movement is -5 km (negative because it is in the opposite direction of north).
Next, let's consider the movement in the east-west direction. The man walks 3 km in the direction 60 degrees west of south. This means that if we draw a line from the starting point to the end point of this movement, it would be at an angle of 60 degrees with the line pointing south.
To find the east-west component, we can use trigonometry. We know that the 60-degree angle is opposite the east-west component, and the hypotenuse of the triangle is 3 km. So, we can use the sine function to find the east-west component:
east-west component = 3 km * sin(60 degrees) = 3 km * 0.866 = 2.598 km (approximately)
Now, we can add up the north-south and east-west components:
total distance from the starting point = square root((north-south component)^2 + (east-west component)^2)
total distance from the starting point = square root((-5 km)^2 + (2.598 km)^2)
total distance from the starting point = square root(25 km^2 + 6.744 km^2)
total distance from the starting point = square root(31.744 km^2)
total distance from the starting point ≈ 5.63 km (approximately)
Therefore, the man is at a distance of approximately 5.63 km from the starting point.