A boy walks 1260meters on a bearing of 120°.how far South is he from the starting point?show all workings including drawing
All angles are measured CW from +Y-axis.
1260m[120o] = distance traveled.
Y = 1260*Cos120 = -630 = 630 m., South.
for CW rotation(bearing), we are in Q2.
In my sketch I have a triangle in the 4th quadrant with a hypotenuse of 1260 and
a base angle of 30° trying to find the y value
sin30° = y/1260
y = 1260sin39° metres.
Be careful how you word your answer, remember that your value is negative
in quadrant 4. However, if you use the word "south" you don't show the negative sign.
To find how far south the boy is from the starting point, we need to break down the given information and perform some calculations. Here are the steps to find the answer along with a drawing:
Step 1: Draw a diagram:
Draw a scale diagram with an arrow indicating the starting point and direction. Label it as point A. Mark an angle of 120° from the starting point.
A
↙︎ 120°
Step 2: Calculate the adjacent side length:
The direction given is 120°, which means it is measured from the North (upward direction). To find the adjacent side length (the side parallel to the North-South direction), calculate the cosine of the given angle.
Adjacent side length (AC) = Cos(120°) * distance walked
Step 3: Substitute the values and calculate:
The distance walked is given as 1260 meters.
AC = Cos(120°) * 1260
Using a scientific calculator or online calculator, find the cosine of 120°, which is -0.5.
AC = (-0.5) * 1260
AC = -630 meters
The negative sign indicates that the position is in the opposite direction to North.
Step 4: Determine the final answer:
As we found AC to be -630 meters, it means the boy is 630 meters south from the starting point.
So, the boy is 630 meters south from the starting point.
Note: If you have a protractor or compass, you can also draw a more accurate diagram by measuring the angle precisely.