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 18�

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): You can put this solution on YOUR website!
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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.

Solved.

Answer by math_tutor2020(3816) (Show Source): 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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