The angle of depression represents the angle from a horizontal layout to a lower surface. The distance between the two stadiums is 3115.1 meters
The given parameters have been illustrated using the attached image of triangles.
The stadiums are represented with A and B.
First, calculate distance BO using:
[tex]\tan T =\frac{BO}{TO}[/tex]
Where:
[tex]\angle T = 90 -75.2 = 14.8[/tex]
[tex]TO = 1100[/tex]
So, we have:
[tex]\tan(14.8^o) = \frac{BO}{1100}[/tex]
Make BO the subject
[tex]BO = 1100 * \tan(14.8^o)[/tex]
[tex]BO = 1100 * 0.2642[/tex]
[tex]BO = 290.62[/tex]
Next, calculate distance AO using:
[tex]\tan T =\frac{AO}{TO}[/tex]
But in this case:
[tex]\angle T = 90 -17.9 = 72.1[/tex]
[tex]TO = 1100[/tex]
So, we have:
[tex]\tan(72.1^o) = \frac{AO}{1100}[/tex]
Make AO the subject
[tex]AO = 1100 * \tan(72.1^o)[/tex]
[tex]AO = 1100 * 3.0961[/tex]
[tex]AO = 3405.71[/tex]
The distance AB between the 2 stadiums is:
[tex]AB = AO - BO[/tex]
[tex]AB = 3405.71-290.61[/tex]
[tex]AB = 3115.1[/tex]
Hence, the distance between the 2 stadiums is 3115.1 meters.
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