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Natalka [10]
3 years ago
14

From where Kiana is standing, she must look up at a 50° angle to see the top of a building. If she backs up 50 feet, she will ne

ed to look up at a 40° angle to see the top of the same building. Approximately how tall is the building?

Mathematics
2 answers:
Morgarella [4.7K]3 years ago
5 0
For this case, what we must do is solve the following system of equations:
 tan (50) = h / x
 tan (40) = h / (x + 50)
 Solving the system we have:
 (x + 50) * tan (40) = h
 (x) * tan (50) = h
 Matching:
 (x + 50) * tan (40) = (x) * tan (50)
 Rewriting:
 x (tan (50) - tan (40)) = 50 * tan (40)
 x = 50 * tan (40) / (tan (50) - tan (40))
 x = 118.9692621
 Substituting:
 h = (x) * tan (50)
 h = (118.9692621) * tan (50)
 h = 141.7820455
 Answer:
 
The height of the building is:
 
h = 141.7820455 ft
Vikentia [17]3 years ago
5 0

Answer:

B. 141.8ft

Step-by-step explanation:

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