SOLUTION: From a second-storey window directly across the street, the angle of elevation of the top of an office building in Makati is 57° 20' and the angle of depression of the base is 18Â
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-> SOLUTION: From a second-storey window directly across the street, the angle of elevation of the top of an office building in Makati is 57° 20' and the angle of depression of the base is 18Â
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Question 1204257: From a second-storey window directly across the street, the angle of elevation of the top of an office building in Makati is 57° 20' and the angle of depression of the base is 18° 10'. If the buildings are 38 m. apart, what is the height of the building? Found 2 solutions by ikleyn, math_tutor2020:Answer by ikleyn(52778) (Show Source):
The height of the building is 38*tan(57° 20') + 38*tan(18° 10') meters.
You calculate the rest.
If you need explanations, make a sketch and recall the definition of the tangent function.
You can put this solution on YOUR website!
57° 20' = 57 + (20/60) = 57.33333° approximately
18° 10' = 18 + (10/60) = 18.16667° approximately
Diagram
The person's eye is located at point A.
B is just across from A.
C and D are the top and base of the other building.
Focus on triangle ABC.
tan(angle) = opposite/adjacent
tan(angle CAB) = BC/AB
tan(57.33333°) = x/38
x = 38*tan(57.33333°)
Now turn your focus to triangle ABD.
tan(angle) = opposite/adjacent
tan(angle DAB) = BD/AB
tan(18.16667°) = y/38
y = 38*tan(18.16667°)
The total height of CD is
CD = CB + BD
CD = x + y
CD = 38*tan(57.33333°) + 38*tan(18.16667°)
CD = 38*( tan(57.33333°) + tan(18.16667°) )
CD = 71.73617
The building is roughly 71.736 meters tall.
Round this approximate value however your teacher instructs.
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