Leon is standing $60$ feet from a telephone pole. As he looks up, a red-tailed hawk lands on the top of the pole. Leon’s angle of sight up to the bird is $22^\circ$ and his eyes are $5.2$ feet above the ground.  

1. Draw a detailed picture of this situation. Label it with all of the given information.

   Step 1(a):

   Draw Leon, the telephone pole, and the hawk.

   Step 2(a):

   Draw sight and distance lines.

   Step 3(a):

   Label the known distance(s) and angle(s). Label the unknown height of the telephone pole $x$.

   

   

   

2. How tall is the pole? Show all of your work.

   Hint (b):

   Use the tangent ratio to write an equation and solve for $x$.

   $\text{tan}(22^\circ)=\left(\frac{x}{60}\right)$

   Answer (b):

   $60·\tan(22^\circ)=x$
   $24.24\approx x$
   $\text{height of pole}\approx24.24+5.2\approx29.44\ \text{pies}$