SOLUTION: alice, who is 1.2m tall, is standing of 12m from a building as shown. From her point of view, the angel of view for the top and bottom of the building is 41 degrees. how tall is th

Algebra ->  Trigonometry-basics -> SOLUTION: alice, who is 1.2m tall, is standing of 12m from a building as shown. From her point of view, the angel of view for the top and bottom of the building is 41 degrees. how tall is th      Log On


   

Question 824278: alice, who is 1.2m tall, is standing of 12m from a building as shown. From her point of view, the angel of view for the top and bottom of the building is 41 degrees. how tall is the building to the nearest tenth of a metre?
Answer by TimothyLamb(4379) About Me  (Show Source):
You can put this solution on YOUR website!
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use similar right triangles:
from top of Alice's head to the building, and
from base of building to Alice's feet along the ground
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tanA = opp/adj
tanA = 1.2/12
A = arctan( 1.2/12 )
A = 5.710593137499643 degrees
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use right triangle from top of Alice's head to the building, then up to the top of the building:
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B = 41 - 5.710593137499643
B = 35.289406862500357 degrees
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tanB = opp/adj
tanB = opp/12
opp = 12*tanB
opp = 12*tan(35.289406862500357)
opp = 8.493143180846317 m
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answer:
building height = opp + 1.2
building height = 8.493143180846317 + 1.2
building height = 9.693143180846317
building height = 9.7 m
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