Final answer:
To calculate the tower's height, trigonometry is used to set up two right-angled triangles based on the given angles of elevation and depression.
Step-by-step explanation:
To calculate the height of the tower using the angles of elevation and depression, we can use trigonometry. We'll set up two right-angled triangles - one from the observer to the top of the tower and another from the observer to the base of the tower. The horizontal distance from the observer to the tower can be assumed to be the same for both these triangles. Let's define the height of the tower as 'h', the height of the window above the ground as 'a', and the horizontal distance as 'd'.
For the angle of elevation (39°) to the top of the tower, we can write the following equation using the tangent function: tan(39°) = (h + a) / d. This can be rearranged to d = (h + a) / tan(39°).
For the angle of depression (25°) to the base of the tower, we use: tan(25°) = a / d. Since we calculated the value of 'd' from the angle of elevation, we can substitute that value into this equation, giving us: a = d × tan(25°).
Combining the two equations by substituting d in terms of (h + a) from the first equation into the second one, we can solve for 'h', the height of the tower. Since we don't have a numeric value for the height of the building or the window, we won't get an exact value for the height of the tower without further information.
In practice, if we knew the height of the window ('a') from the ground, we would be able to calculate the height of the tower 'h' by solving this system of equations. But without the numerical height of the window or tower, we can only provide the method for calculating it, not the exact height.