Question

a man standing near a radio station antenna observes that the angle of elevation to the top of the antenna is 64 degrees. He then walks 100ft further away and observes that the angle of elevation to the top of the antenna is 46 degrees. Find the height of the antenna to the nearest foot.

Answer 1

So hmm notice the picture below

thus  $\bf \cfrac{y}{tan(64^o)}=\cfrac{y}{tan(46^o)}-100\implies \cfrac{y}{tan(64^o)}-\cfrac{y}{tan(46^o)}=-100 \\\\\\ y\left[ \cfrac{1}{tan(64^o)}-\cfrac{1}{tan(46^o)} \right]=-100\implies y=\cfrac{-100}{\frac{1}{tan(64^o)}-\frac{1}{tan(46^o)}}$

make sure your calculator is in Degree mode, since the angles are in degrees