A man walk 5km south and then 3km in the direction 60°west of south. His distance from the starting point is
To find the distance from the starting point, we can use the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the man walked 5 km south, which can be considered as the opposite side of a right triangle, and 3 km in the direction 60° west of south, which can be considered as the adjacent side of the triangle. The distance from the starting point can be considered as the hypotenuse.
To find the distance from the starting point, we need to find the length of the hypotenuse. We can use trigonometric functions to solve this.
First, let's find the length of the adjacent side. We know that the man walked 3 km in the direction 60° west of south. From the given information, we can deduce that the angle between the adjacent side and the hypotenuse is 30° (90° - 60°). We can use the cosine function to find the length of the adjacent side.
Adjacent side = 3 km * cos(30°)
Adjacent side ≈ 3 km * 0.866
Adjacent side ≈ 2.598 km
Now, we can use the Pythagorean Theorem to find the length of the hypotenuse (distance from the starting point).
Hypotenuse² = Opposite side² + Adjacent side²
Hypotenuse² = (5 km)² + (2.598 km)²
Hypotenuse² ≈ 25 km² + 6.744 km²
Hypotenuse² ≈ 31.744 km²
Taking the square root of both sides to find the hypotenuse:
Hypotenuse ≈ √31.744 km²
Hypotenuse ≈ 5.64 km
Therefore, the man's distance from the starting point is approximately 5.64 km.