The angle of depression of two points on opposite sides of a building are on the same horizontal level with the foot of the buiding are 58 and 49 respectively from the top of the building. If the building is 38m tall, calculate the distance between the points.

To solve this problem, we can use trigonometry and the concept of angle of depression.

Let's call the distance between the foot of the building and the first point A, and the distance between the foot of the building and the second point B. The angle of depression for the first point is 58 degrees, and for the second point is 49 degrees.

First, let's calculate the height of the building that is above each point. We know that the total height of the building is 38m. Using trigonometry, we can calculate the height above the first point as follows:

Height above the first point = building height / tan(angle of depression for the first point)
Height above the first point = 38m / tan(58 degrees)

Using a scientific calculator, we find that the height above the first point is approximately 32.65m.

Similarly, we can calculate the height above the second point:

Height above the second point = building height / tan(angle of depression for the second point)
Height above the second point = 38m / tan(49 degrees)

Using a scientific calculator, we find that the height above the second point is approximately 44.14m.

Now, we can calculate the horizontal distance between the two points by subtracting the two distances from the total distance between the two points.

Distance = total distance - (distance to the first point + distance to the second point)

Since the two points are at the same horizontal level, we can assume that the total distance between them is equal to the distance between their respective heights above the building.

Distance = height above the first point - height above the second point
Distance = 32.65m - 44.14m

Calculating the difference, we get approximately -11.5m. However, the distance cannot be negative, so we take the absolute value:

Distance = | -11.5m |

Therefore, the distance between the two points is approximately 11.5 meters.

distance= 38(tan58+tan49)

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