a man walks 50m on a bearing 25 degree and then 200m due east.how far is she from her starting point
You do not walk on a bearing but on a heading. Math texts are not written by navigators. Bearing is the direction from you to a object like a lighthouse.
North distance = 50 cos 25
= 45.3
East distance = 50 sin 25 + 200
= 221
distance = sqrt(45.3^3+221^2)
To find out how far the person is from their starting point, we can use the concept of vector addition. We can break down the person's movements into two vectors: one for the 50m walk at a bearing of 25 degrees, and another for the 200m due east.
First, let's find the horizontal and vertical components of the 50m walk at a bearing of 25 degrees. The horizontal component can be found by multiplying the magnitude (50m) by the cosine of the angle (25 degrees). The vertical component can be found by multiplying the magnitude by the sine of the angle.
Horizontal component = 50m * cos(25 degrees) ≈ 45.09m
Vertical component = 50m * sin(25 degrees) ≈ 21.56m
Next, let's add the horizontal component (45.09m) to the 200m due east to get the total horizontal displacement. Since they are both in the same direction, we simply add their magnitudes.
Total horizontal displacement = 45.09m + 200m = 245.09m
Since the horizontal displacement is due east, there is no vertical displacement in this direction.
Now, we can find the distance from the starting point using the Pythagorean theorem. The distance is the hypotenuse of a right triangle formed by the horizontal and vertical displacements.
Distance = √(horizontal^2 + vertical^2)
Distance = √(245.09m^2 + 0^2)
Distance = √(60048.6081m^2)
Distance ≈ 245.08m
Therefore, the person is approximately 245.08 meters away from their starting point.