Answer:
The height is 35.6 meters
Explanation:
This can be translated to:
In the position i am in, the view of tower of the church forms an angle of 52° with the horizontal.
If i walk away a distance of 25m, the angle is 34°.
What is the height of the tower?
Here we have triangle rectangles.
If the initial distance to the tower is X and the height is Y, we have that, using the rule:
Tan(θ) = opposite cathetus/adjacent cathetus
Where X is the adjacent cathetus and Y is the opposite cathetus.
Then we have the system of equations:
Tan(52°) = Y/X
Tan(34°) = Y/(X + 25)
Where we want to find the value of Y.
We can isolate X in the first equation and get:
X = Y/Tan(52°)
and replace it in the other equation:
Tan(34°) = Y/(Y/Tan(52°) + 25)
Tan(34°)*(Y/Tan(52°) + 25) = Y
Y*(Tan(34°)/(Tan(52°)) + Tan(34°)*25 = Y
Tan(34°)*25 = Y - Y*(Tan(34°)/(Tan(52°)) = Y*( 1 - (Tan(34°)/(Tan(52°)))
Y = Tan(34°)*25/(1-Tan(34°)/(Tan(52°)) = 35.6
So the height of the tower is 35.6 meters