Answer:
a) 38.82 m
b) 24.86 m
Step-by-step explanation:
The relevant trig relations are ...
Cos = Adjacent/Hypotenuse
Tan = Opposite/Adjacent
We assume you intend the angle of elevation to be 37°, not 37". (The latter would make the building height be 1.506 m.)
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a)
The distance from the transit to the top of the building is the hypotenuse of the right triangle whose legs are the distance to the building and the height of the building above the transit. Using the cosine relation, we have ...
Hypotenuse = Adjacent/Cos
distance from transit to building top = (31 m)/cos(37°) ≈ 38.82 m
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b)
The height of the building above the transit can be found using the tangent relation.
additional height = (31 m)tan(37°) ≈ 23.36 m
So, the height of the building is about ...
23.36 m + 1.5 m = 24.86 m
