SOLUTION: 1. From a second - story window directly across the street, the angle of elevation of the top of an office building is 57 degrees and 20 minutes and the angle of depression of the
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Question 579894: 1. From a second - story window directly across the street, the angle of elevation of the top of an office building is 57 degrees and 20 minutes and the angle of depression of the base is 18 degrees and 10 minutes. If the buildings are 38 m. apart, what is the height of the building ?
2. Mr. Reyes wanted to know the height of the tree. What he did was form a point A on the ground and observed that the angle of elevation of the top of the tree was 30 degrees. He then moved 50 ft. away from A. In his second position at B, the angle of elevation of the top of the tree was 22 degrees. Find the height of the tree. Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website! angle of elevation = 57 deg 27 mins
distance from the window = 38 m
let the height of office be h
Let the vertical heightbetween the window and the office be x feet.
height of office upto level of window=
Tan 57 27' = x/38
angle of depression is 18 10'
vertical height of window from the ground = (h-x)
Tan 18 10' = (h-x)/38
Tan 57 27'+Tan 18 10' = (h-x)/38 + x/38
Tan 57 27'+Tan 18 10'= h/38 -x/38 +x/38
Tan 57 27'+Tan 18 10' = h/38
Tan 57.45 + Tan 18.17 = h/38
1.57 + 0.33 = h/38
1.9= h/38
h= 1.9 *38
h= 72.2 m
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From point A angle of elevation = 30 deg
From point B angle of elevation = 22 deg
distance AB = 50 ft.
let height of tree be h
and distance from point A be x
Tan 30 = h/x
Cot 30 = x/h
Point B
Tan 22 = h/(50+x)
cot 22 = (50+x)/h
Cot 22- Cot 30 = 50/h +x/h - x/h
2.475-1.733= 50/h
0.742= 50/h
h= 50/0.742
67.38 feet
