solve a point p is 45 km from q on a bearing 75°. how far is p north of q
75 degrees clockwise from North
45 cos 75 = 11.6
A point p is 45km from Q on a bearing of 75'.How far is P north of Q
To determine how far point P is north of point Q, we need to find the component of the distance in the north direction.
We can begin by creating a right-angled triangle using point P, point Q, and the north direction. The angle between the north direction and the bearing is the complement of 75°, which is 90° - 75° = 15°.
Now, we can use trigonometry to find the distance north of Q. Let's label the distance north as N.
Using the sine function, we have:
sin(15°) = N / 45 km
Rearranging the equation to solve for N, we get:
N = 45 km * sin(15°)
Using a scientific calculator to evaluate sin(15°), we get:
N ≈ 45 km * 0.2588
Calculating the product, we find:
N ≈ 11.65 km
Therefore, point P is approximately 11.65 km north of point Q.
To find how far point P is north of point Q, we need to determine the north component of the distance.
First, let's understand the given information. We know that point P is 45 km away from point Q on a bearing of 75°. The bearing represents the angle between the line connecting Q to P and the north direction.
To find the north component, we can use trigonometry. Specifically, we can use the sine function since it relates the opposite side (north component) to the hypotenuse (distance between P and Q).
To do this, we'll follow these steps:
1. Draw a diagram, labeling point Q and point P.
2. Mark the north direction on the diagram.
3. Mark the angle of 75° from the line connecting Q to P.
4. Identify the north component as the side opposite to the angle (label it as "N").
5. Label the hypotenuse as the given distance of 45 km.
6. Apply the sine function: sin(angle) = N / hypotenuse.
In this case, sin(75°) = N / 45 km.
7. Rearrange the equation to solve for N: N = sin(75°) * 45 km.
8. Use a calculator to evaluate sin(75°) and multiply the result by 45 km to find N.
By following these steps, you can find the north component (N) and determine how far point P is north of point Q.