SOLUTION: From the top of an 80-ft building, the angle of elevation of the top of a taller building is 49 and the angle of depression of the base of this building is 62 degrees. Determine th

Algebra ->  Linear-equations -> SOLUTION: From the top of an 80-ft building, the angle of elevation of the top of a taller building is 49 and the angle of depression of the base of this building is 62 degrees. Determine th      Log On


   

Question 1105223: From the top of an 80-ft building, the angle of elevation of the top of a taller building is 49 and the angle of depression of the base of this building is 62 degrees. Determine the height of the taller building to the nearest foot.
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
Approach: the angle of depression can be used to find the distance over to the other building. Then the distance to the other building and angle of elevation are used to find the height of the other building (well, the "extra" height y beyond 80ft).
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sin(90-62)/d = sin(62)/80
d = (sin(28)/sin(62))*80 = 42.537ft
sin(41)/42.537 = sin(49)/y
y = (sin(49)/sin(41))*42.537 = 48.722ft
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Height of other building = 80ft + 48.722ft = 128.722ft
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Ans: Rounded to nearest foot, the other building is 129ft tall
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