A tree is 8km due south of a building. Kofi is standing 8km west of the tree. Find the bearing of Kofi from the building

Answer Details

To find the bearing of Kofi from the building, we need to draw a diagram and use trigonometry.

        K
        |
        |
        |
        T
       /
      /
     /
    B

We know that the tree is 8km due south of the building, so we can draw a line segment from B to T, and label it 8km.

        K
        |
        |
        |
        T
       / \
      /   \
     /     \
    B-------T
         8km

We also know that Kofi is standing 8km west of the tree, so we can draw a line segment from K to T, and label it 8km.

        K
        |
        |
        | 8km
        T
       / \
      /   \
     /     \
    B-------T
         8km

Now, we can use trigonometry to find the bearing of Kofi from the building. We know that Kofi is west of the tree, so the bearing we want is the angle between the line segment BT and the line segment BK. We can use the tangent function to find this angle:

tan(theta) = opposite / adjacent

tan(theta) = BT / BK

tan(theta) = 8km / 8km

theta = tan-1(1)

theta ≈ 45°

So the angle between BT and BK is approximately 45 degrees. Since Kofi is west of the tree, we know that the bearing of Kofi from the building is 180 degrees plus 45 degrees, or 225 degrees.

Therefore, the answer is (c) 225^o.