Question 1206177: You are 12.5 meters away from a 2-story residential building with an approximate height of 7 meters. At the same time, you are 21 meters away from the church, how high is the church? Provide an illustration and a Solution
Found 3 solutions by Theo, math_tutor2020, ikleyn:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! if you assume that the church is in the same line as the 2 story residential building and that the angle of elevation from you to the building is the same angle of elevation from you to the church, then you have 2 similar right triangles that have equal angles and have proportional sides.
here's my diagram.
ddddd
the angle of elevation is T.
tan(T) = 7/12.5 and tan(T) = x/21.
since they are both equal to tan(T), then they are equal to each other and you get 7/12.5 = x/21.
cross multiply to get 7*21 = 12.5*x
solve for x to get x = 7*21/12.5 = 11.76.
11.76 is the height of the church.
T is equal to arctan(7/12.5) and arctan(11.76/21).
use your calculator to find that T = 29.24882634 degrees in both cases.
here's my diagram.
Answer by math_tutor2020(3817)  (Show Source):
You can put this solution on YOUR website!
The wording of your question is a bit vague.
If tutor @Theo has the correct diagram, then follow the steps shown below:
x/7 = 21/12.5
12.5x = 7*21
x = 7*21/12.5
x = 11.76
The church would have an appoximate height of roughly 11.76 meters.
The initial ratio in the 1st step is valid because of the similar triangles.
Answer by ikleyn(52781)  (Show Source):
You can put this solution on YOUR website! .
For the future generations of students, who will read this post.
The problem's formulation in the post is FATALLY incomplete,
since it does not have a key description, connecting the two objects.
So, do not consider it seriously.
And never formulate your problems this way.
Respect yourself and respect the tutors.
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