A man goes 7m east and then 24m to south. Find his distance from the starting point
Let x = distance
Hint: Draw a diagram. You should realise it's Pythagoras theorem
x^2 = 7^2 + 24^2
x^2 = 625
x = 25
Answer: 25m SE
A man walks 10 km West, gets some rest, and continues for another 7 km in the same direction
To find the distance from the starting point, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the man goes 7m east and then 24m to the south. This forms a right triangle, with the distance from the starting point as the hypotenuse.
We can label the sides of the triangle as follows:
- The east side as side A, with a length of 7m.
- The south side as side B, with a length of 24m.
- The distance from the starting point as the hypotenuse, which we can label as side C.
Using the Pythagorean theorem, we have the equation:
C² = A² + B²
Plugging in the given values, we have:
C² = 7² + 24²
C² = 49 + 576
C² = 625
To find the value of C, we take the square root of both sides:
C = √625
C = 25
Therefore, the man is 25m away from the starting point.