The angle of depression is the angle between the line of sight and a vertical line.
The distance between the two skyscrapers is 1269ft
I've added as an attachment, a figure that illustrates the scenario
First, we calculate distance AB using the following tangent ratio
[tex]\mathbf{\tan(\theta) = \frac{Opposite}{Adjacent}}[/tex]
So, we have:
[tex]\mathbf{\tan(60) = \frac{AB}{1250}}[/tex]
Make AB the subject
[tex]\mathbf{AB = 1250 \times \tan(60)}[/tex]
Next, we calculate distance AC using the following tangent ratio
[tex]\mathbf{\tan(\theta) = \frac{Opposite}{Adjacent}}[/tex]
So, we have:
[tex]\mathbf{\tan(60+10) = \frac{AB + BC}{1250}}[/tex]
[tex]\mathbf{\tan(70) = \frac{AB + BC}{1250}}[/tex]
Make AB + BC, the subject
[tex]\mathbf{AB + BC = 1250 \times \tan(70)}[/tex]
Make BC the subject
[tex]\mathbf{BC = 1250 \times \tan(70) - AB}[/tex]
Substitute [tex]\mathbf{AB = 1250 \times \tan(60)}[/tex]
[tex]\mathbf{BC = 1250 \times \tan(70) - 1250 \times \tan(60)}[/tex]
[tex]\mathbf{BC = 1269}[/tex]
Hence, the distance between the two skyscrapers is 1269ft
Read more about angles of depression at:
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