+0

# 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?

0
222
1

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
Sort:

#1
+18777
+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

### 5 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details