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

#1**+5 **

**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