# a point P is 45 km from Q on a bearing of 75°. how far is P north of Q correct to two significant figures

## did you make a sketch??

looks like a simple .... sin15° = y/45
y = 45sin15° = ....

## To find how far point P is north of point Q, we need to determine the component of the displacement (distance) along the north direction.

Given:
Distance between point P and point Q = 45 km
Bearing of point P from point Q = 75°

To find the north component, we need to find the sine of the angle between the bearing and the north direction (which is 15°, as the bearing is measured clockwise from the north).

Using the sine function:
sin(15°) = north component / distance between P and Q

We can rearrange the equation to solve for the north component:
north component = sin(15°) * distance between P and Q

north component = sin(15°) * 45 km

Using a calculator, sin(15°) ≈ 0.2588

north component ≈ 0.2588 * 45 km

north component ≈ 11.65 km

Therefore, point P is approximately 11.65 km north of point Q, correct to two significant figures.

## To find how far point P is north of point Q, we need to break down the given information.

The bearing of 75° means that Q is located 75° clockwise from the north direction. Therefore, we can say that Q lies 75° east of north.

Let's draw a diagram to visualize the situation:

N

45 km 75° │
· P Q

Using basic trigonometry, we know that the northward distance (d) can be found using the formula:

d = distance * sin(angle)

Here, the distance is given as 45 km, and the angle is 75°.

Applying the formula:

d = 45 km * sin(75°)

Using a scientific calculator, we can calculate:

d ≈ 44.3 km

Therefore, point P is approximately 44.3 km north of point Q, correct to two significant figures.