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?
+26367 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?
\(Let\ x = \text{ height of the bridge}\)
\(\begin{array}{|rcll|} \hline \tan(20^{\circ}) &=& \frac{x-6 }{100 } \\ 100\cdot \tan(20^{\circ}) &=& x-6 \\ 6 + 100\cdot \tan(20^{\circ}) &=& x \\ x &=& 6 + 100\cdot \tan(20^{\circ}) \\ x &=& 6 + 100\cdot 0.36397023427 \\ x &=& 6 + 36.3970234266 \\ \mathbf{x} & \mathbf{=} & \mathbf{42.3970234266\ \text{feet}} \\ \hline \end{array} \)
