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An airship has an altitude of 800 m. In a distance, a village is seen with an angle of depression...

Question:

An airship has an altitude of 800 m. In a distance, a village is seen with an angle of depression of 12°. Find the distance of the airship from the village.

Tangent Ratio:

The tangent of an angle is the relationship between the opposite leg and the adjacent leg. Rectangular triangles are perfect for learning about complementary angles. We already know that an internal angle is {eq}90{/eq} degrees, while the other two are not, but the sum of this has to be equal to {eq}90{/eq} degrees to have an internal sum of {eq}180{/eq} degrees.

Answer and Explanation:

$$\begin{align*} \tan 12^{\circ}&=\frac{800\: \rm m}{k} \\[0.3cm] k&=\frac{800\: \rm m}{\tan 12^{\circ}} \\[0.3cm] k&\approx 3763.70\: \rm m \end{align*} $$


The distance of the airship from the village is approximately {eq}3763.70 \ \rm meters{/eq}.


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