From an observation tower that overlooks a runway, the angles of depression of point A, on one side of the runway, and point B, on the opposite side of the runway are, and , respectively. The points and the tower are in the same vertical plane and the distance from A to B is 1.1 km. Determine the height of the tower.
Please verify if 72.2 meters is the height of the tower.
your angles are missing.
To find the height of the tower, we can use trigonometry and the concept of angles of depression.
Let's assume the height of the tower is represented by 'h' (in meters).
From the top of the tower, we have an angle of depression to point A and point B. Angle of depression is the angle formed between the horizontal line and the line of sight from the observer to the point below.
We can use the tangent function (tan) to relate the angles of depression to the height of the tower.
For point A, we have the angle of depression (angle 1) and for point B, we have the angle of depression (angle 2).
Using trigonometry, we can write the following equations:
tan(angle 1) = h / distance from tower to point A
tan(angle 2) = h / distance from tower to point B
Given that the distance from point A to point B is 1.1 km (or 1100 meters), we can solve these equations to find the value of 'h'.
Let's substitute the given values into the equations:
tan(angle 1) = h / 1100
tan(angle 2) = h / 1100
Now, we need to know the values of angle 1 and angle 2 to proceed with the calculations. Please provide the values of angle 1 and angle 2 so that we can find the correct height of the tower.