Sketched this Bearing
A survey leaves a base camp and drives 42km on a bearing of 032 degree, she then drive 28km on a bearing, if 154 degree. How far is she from her base?
You take a bearing. You travel on a heading.
DRAW THIS !!!
call starting point A
second point B at 32 deg from north toward east, 42 km
third Point C at 180 - 154 = 26 deg from south toward east
so Angle ABC at B is 32 + 26 = 58 deg
now we have angle of 58 deg between triangle lengths of 42 and 28
That is law of cosines to find the third side.
b^2 = a^2 + c^2 - 2 a c cos 58
b^2 = 28^2 + 42^2 - 2 * 28 * 42 * 0.53
solve for b
Please I really need to know this answer
Correct👍👍👍
The question is not correct 🙂
To find the distance from the base camp, we can use the concept of vector addition.
First, let's draw a sketch of the situation. Start by placing the base camp at the origin (0, 0) on a coordinate plane.
The surveyor drives 42 km on a bearing of 032 degrees. To represent this, draw a line segment of length 42 units at an angle of 32 degrees from the positive x-axis.
Next, the surveyor drives 28 km on a bearing of 154 degrees. Draw another line segment of length 28 units at an angle of 154 degrees from the positive x-axis.
Now, we can find the horizontal and vertical components of each line segment.
For the first line segment (42 km on a bearing of 032 degrees):
- The horizontal component is calculated using the formula: distance * cos(angle).
horizontal component = 42 km * cos(32 degrees).
- The vertical component is calculated using the formula: distance * sin(angle).
vertical component = 42 km * sin(32 degrees).
For the second line segment (28 km on a bearing of 154 degrees):
- The horizontal component is calculated using the formula: distance * cos(angle).
horizontal component = 28 km * cos(154 degrees).
- The vertical component is calculated using the formula: distance * sin(angle).
vertical component = 28 km * sin(154 degrees).
Now, sum up the horizontal components and the vertical components separately.
- To calculate the total horizontal component, add the horizontal components of both line segments.
- To calculate the total vertical component, add the vertical components of both line segments.
Finally, calculate the distance from the base camp using the Pythagorean theorem:
distance = sqrt((total horizontal component)^2 + (total vertical component)^2)
Evaluate this equation to find the distance from the base camp.