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| Math Central | Quandaries & Queries |
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Question from Andrew: If an antenna is atop a building 70 feet tall and the antenna has a beam width of 30 degrees how far from the building does the beam first touch the ground? |
Hi Andrew,
I drew a diagram of want you described.
$AD$ is parallel to the ground and $CD$ is perpendicular to the ground so that triangle $CDA$ is a right triangle. $|AB| = |DC| = 70$ feet and the measure of the angle $DAC$ is $\large \frac{30}{2} \normalsize = 15$ degrees. $|AD| = |BC|$ is the length required.
What trig function relates the measure of the angle $DAC$ to $|DA|$ and $|CD|?$
Penny
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