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7 days ago

8

A blimp is 1100 meters high in the air and measures the angles of depression to two stadiums to the west of the blimp. If those

measurements are 75.2° and 17.9°, how far apart are the two stadiums?

1 answer:

tester [12.3K]7 days ago

8 0

Answer:

The distance separating the two stadiums is nearly 3115.1 meters

Step-by-step explanation:

By creating two right angle triangles formed between the blimp and each stadium, as illustrated in the provided image, the spatial separation "x" can be calculated as the excess length of the ground-level triangle legs.

To calculate the lengths of these legs, the tangent function corresponding to the given depression angles can be applied as follows:

$tan(75.2^o)=\frac{1100}{a} \\a=\frac{1100}{tan(75.2^o)}\\a\approx 290.6\,\,meters$

and for the other one:

$tan(17.9^o)=\frac{1100}{b} \\b=\frac{1100}{tan(17.9^o)}\\b\approx 3405.7\,\,meters$

Therefore, the separation between the stadiums is determined by the calculation:

b - a = 3405.7 - 290.6 meters = 3115.1 meters

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