Answer
$21.67$ feet
Work Step by Step
The trigonometric ratios are as follows: $\sin \theta= \dfrac{opposite}{hypotenuse}$ ; $\cos \theta= \dfrac{Adjacent}{hypotenuse}$ and $\tan \theta= \dfrac{Opposite}{Adjacent}$
Let $ a $ be the height of the antenna.
Height of the taller building $=d+40$ yards
Then: $ d=125 \times \cot 68^{\circ} $ and $ d=(125+a) \cot 71^{\circ}$
So, $ a=\dfrac{125 ( \cot 68^{\circ} -\cot 71^{\circ})}{\cot 71^{\circ}}=21.67 feet $
