+0  
 
0
457
1
avatar

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
avatar+20009 
+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?

 

\(Let\ x = \text{ height of the bridge}\)

 

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

 

 

laugh

heureka  Mar 14, 2017

10 Online Users

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.