# Chapter 4 - Review Exercises - Page 646: 121

$21.67$ 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, $a=\dfrac{125 ( \cot 68^{\circ} -\cot 71^{\circ})}{\cot 71^{\circ}}=21.67 feet$

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