A HOSPITAL(H) IS 7KM EAST AND 5KM NORTH OF A SCHOOL(S). CALCULATE THE BEARING OF H FROM S

a = tanh(7/5) = 54.5

To calculate the bearing of H (hospital) from S (school), we can use trigonometry.

Step 1: Draw a diagram showing the positions of the hospital (H) and the school (S).

```
N
|
|
|
|
-------S-------->
|
|
|
|
H
```

Step 2: Calculate the distance in the horizontal (east-west) direction between H and S. Since H is 7 kilometers east of S, this distance is 7 km.

Step 3: Calculate the distance in the vertical (north-south) direction between H and S. Since H is 5 kilometers north of S, this distance is 5 km.

Step 4: Use the tangent function to calculate the angle formed by the line joining H and S with the horizontal axis.

```
tan(θ) = opposite/adjacent
tan(θ) = 5/7
```

Step 5: Use the inverse tangent function (arctan) to find the value of θ.

```
θ = arctan(5/7)
```

The approximate value of θ is 36.87 degrees.

Step 6: Determine the quadrant where the angle lies. Since H is to the east and north of S, the angle is in the northeast quadrant.

Step 7: Calculate the bearing angle. The bearing angle is measured clockwise from the north direction, so we have to adjust our angle accordingly.

```
Bearing = 90 degrees - θ
Bearing = 90 - 36.87
Bearing = 53.13 degrees
```

Therefore, the bearing of H from S is approximately 53.13 degrees.

To calculate the bearing of H from S, we can use basic trigonometry.

Step 1: Draw a diagram to visualize the situation.

Let's draw a coordinate system with the school (S) as the origin (0,0). The hospital (H) will be at coordinates (7,5) since it is 7 km east and 5 km north of the school.

Y
^
| H(x=7,y=5)
|
|
| S(0,0)
|------------------------------------> X

Step 2: Calculate the distance (D) between S and H using the Pythagorean theorem.

The distance (D) is the hypotenuse of a right-angled triangle with the vertical side being 5 km and the horizontal side being 7 km.

D = √(7^2 + 5^2)
= √(49 + 25)
= √74
≈ 8.60 km (rounded to two decimal places)

Step 3: Calculate the direction or bearing (θ) from S to H.

To find the bearing, we need to calculate the angle between the direction from S to H and the positive x-axis.

Using trigonometry, we can calculate the tangent of the angle (θ) using the ratio of the vertical side length (5 km) to the horizontal side length (7 km).

tan(θ) = 5/7

To find the angle itself, we can use the inverse tangent (arctan) function:

θ = arctan(5/7)
≈ 37.15 degrees (rounded to two decimal places)

Therefore, the bearing of H from S is approximately 37.15 degrees.

I would think 90