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Two buildings stand 90ft apart at their closest points. At those points the angle of...

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r4rob92 | Valedictorian

Posted May 13, 2013 at 2:50 PM via web

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Two buildings stand 90ft apart at their closest points. At those points the angle of depression from the taller bldg to the shorter bldg is 12 degrees. How much taller is the taller bldg?

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crmhaske | College Teacher | (Level 3) Associate Educator

Posted May 13, 2013 at 3:10 PM (Answer #1)

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Let x = the distance between the two buildings
Let d = the angle of depression
Let y = the difference in height

In the attached diagram, the black lines represent the two buildings, and the red lines represent the triangle that is created when you connect the two buildings by an imaginary line.

The unknown value, y, can be solved using the trigpnometric function tangent:

`tan(d)=(opp)/(adj)=y/x` 

`tan(12)=y/90` 

`y=90*tan(12)=19.1`

Therefore, the difference in height between the tall building and the short building is 19.4 ft.

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