Desde el lugar donde me encuentro, la visual a la torre de una Iglesia forma un ángulo de 52° con la horizontal. si me alejó 25 m más de la torre, el ángulo es de 34°. ¿Cuál es la altura de la torre?

The height is 35.6 meters

Step-by-step 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

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