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# How tall is a bridge if a 6-foot-tall person standing 100 feet away can see the top of the bridge at an angle of 20 degrees to the horizon?

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How tall is a bridge if a 6-foot-tall person standing 100 feet away can see the top of the bridge at an angle of 20 degrees to the horizon?

Guest Mar 14, 2017
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How tall is a bridge if a 6-foot-tall person standing 100 feet away

can see the top of the bridge at an angle of 20 degrees to the horizon?

$$Let\ x = \text{ height of the bridge}$$

$$\begin{array}{|rcll|} \hline \tan(20^{\circ}) &=& \frac{x-6 }{100 } \\ 100\cdot \tan(20^{\circ}) &=& x-6 \\ 6 + 100\cdot \tan(20^{\circ}) &=& x \\ x &=& 6 + 100\cdot \tan(20^{\circ}) \\ x &=& 6 + 100\cdot 0.36397023427 \\ x &=& 6 + 36.3970234266 \\ \mathbf{x} & \mathbf{=} & \mathbf{42.3970234266\ \text{feet}} \\ \hline \end{array}$$

heureka  Mar 14, 2017