A boy walks 1260m on a bearing of 120 degree. How far is he from his starting point with fully detailed diagram.
The user said: A boy walks 1260m
so he is 1260m from his starting point.
I apologize for the mistake in the calculation. You are correct. Since the boy walks 1260m in the given direction, he would be 1260m from his starting point. Thank you for pointing that out.
To find how far the boy is from his starting point, we will use trigonometry to calculate the distance.
Let's label the starting point as point A, and the ending point where the boy ends up as point B. We are given that the boy walks 1260m on a bearing of 120 degrees from his starting point.
Now let's draw a diagram to represent the situation:
1. Draw a horizontal line to represent the ground.
2. Label point A as the starting point.
3. Draw a line segment from point A in the direction of the bearing of 120 degrees. Label the endpoint of this line segment as point B.
4. Draw a perpendicular line from point B to the line representing the ground. Label the point where this perpendicular line intersects the ground as point C.
Now, we have formed a right triangle with sides AB (1260m), BC (the distance we want to find), and AC (the distance from point A to point C).
From the diagram, angle ABC is 120 degrees. Therefore, angle BAC is 180 - 120 = 60 degrees.
We know that the cosine of an angle in a right triangle is equal to the adjacent side divided by the hypotenuse. Therefore, we can write:
cos(60 degrees) = BC / AB
cos(60 degrees) = BC / 1260
BC = 1260 * cos(60 degrees)
BC = 1260 * 0.5
BC = 630m
Therefore, the boy is 630m from his starting point.