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Sine, Cosine, Tangent Applications

The Sine, Cosine and Tangent functions are often applied to real world scenarios.

Example 1

What is the height of the tree below?

Real world Trigonometry

$ tan(16) = \frac{opp}{adj} \\ tan(16) = \frac{14}{\red x} \\ \red x = \frac{14}{tan(16)} \\ \red x = 48.8 $

problem 1

At 57" from the base of a building you need to look up at 55° to see the top of a building. What is the height of the building?

building problem

$ tan(55) = \frac{opp}{adj} \\ tan(55)= \frac{\red x }{ 57} \\ \red x = 57 \cdot tan(55) \\ \red x = 81.4 $


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