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yaroslaw [1]
3 years ago
5

Juliet stands at the window of her apartment so that her eyes are 38.4 feet above the ground. Juliet spots her boyfriend down th

e street a few blocks away. She knows, based off the number of city block, that her boyfriend is at a distance of 156.45 feet away from the building. Determine the angle of depression of juliet’s site to her boyfriend on the ground

Mathematics
1 answer:
romanna [79]3 years ago
6 0

Answer: 13.79\º  

The <u>angle of depression</u> is that which <u>measurement is made between the visual line and the horizontal line</u> (figure attached), <u>taking into account that the object that forms the angle is below the horizontal</u>.

In additon, this angle is congruent with the elevation angle.

In the attached figure we can see the situation described in the statement:

The figure formed is a right triangle with two known sides. We can use the tangent trigonometric function to find the value of the angle \theta, as follows:

tan(\theta)=\frac{OC}{AC}  

Where OC=38.4ft is the opposite cathetum or leg to the angle \theta, and  AC=156.45ft is the adjacent cathetum or leg to \theta.

Then:

tan(\theta)=\frac{38.4}{156.45ft}  

tan(\theta)=0.245  

\theta=arctan(0.245)  

Finally we find the angle of depression of Juliet’s site to her boyfriend on the ground:

\theta=13.79\º  

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