Angle of elevation measured for a tower erected over a building from a point of aninstrument located on the ground was 12° and 9° for the top and bottom of the towerrespectively. The height of the tower is 9 m. If the angle at depression of plinth level ofthe building from the same instrument is 4°, calculate the height of the building. (7Marks)

To solve this problem, we will use the concept of trigonometry. Here are the steps:

1. First, we need to find the distance from the instrument to the building. We know that the angle of elevation to the top of the tower is 12° and to the bottom of the tower is 9°. The difference between these angles (12° - 9° = 3°) corresponds to the height of the tower, which is 9m.

2. We can use the tangent of the angle of elevation to the bottom of the tower (9°) to find this distance. The tangent of an angle in a right triangle is the ratio of the opposite side (the height) to the adjacent side (the distance we want to find). So, we have:

   tan(9°) = height / distance distance = height / tan(9°) distance = 9m / tan(9°)

3. Now, we can find the height of the building. We know that the angle of depression to the plinth level of the building is 4°. The angle of depression is the same as the angle of elevation from the point of view of the instrument, so we can use the tangent of this angle to find the height of the building. We have:

   tan(4°) = height / distance height = distance * tan(4°)

4. Substitute the value of the distance we found in step 2 into this equation to find the height of the building.

Remember to use the correct units for your answer.