c) $ \tan 75 ^ { circ } = \frac { h } { 5.5 } $

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Accepted Answer

# Explanation:
## Step1: Solve for $ h $
Multiply both sides of the equation $ \tan75^{\circ}=\frac{h}{5.5} $ by $ 5.5 $.
$$h = 5.5\times\tan75^{\circ}$$
## Step2: Calculate $ \tan75^{\circ} $
We know that $ \tan(A + B)=\frac{\tan A+\tan B}{1-\tan A\tan B} $, and $ 75^{\circ}=45^{\circ}+30^{\circ} $.
$$
\begin{align*}
\tan75^{\circ}&=\tan(45^{\circ}+ 30^{\circ})\
&=\frac{\tan45^{\circ}+\tan30^{\circ}}{1-\tan45^{\circ}\tan30^{\circ}}\
&=\frac{1+\frac{\sqrt{3}}{3}}{1 - 1\times\frac{\sqrt{3}}{3}}\
&=\frac{\frac{3 + \sqrt{3}}{3}}{\frac{3-\sqrt{3}}{3}}\
&=\frac{3+\sqrt{3}}{3-\sqrt{3}}\
&=\frac{(3 + \sqrt{3})(3+\sqrt{3})}{(3-\sqrt{3})(3+\sqrt{3})}\
&=\frac{9+6\sqrt{3}+3}{9 - 3}\
&=\frac{12 + 6\sqrt{3}}{6}\
&=2+\sqrt{3}\approx3.732
\end{align*}
$$
## Step3: Calculate $ h $
Substitute $ \tan75^{\circ}\approx3.732 $ into $ h = 5.5\times\tan75^{\circ} $.
$$h\approx5.5\times3.732 = 20.526$$

# Answer:
$ h\approx20.53 $

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Question

Explanation:

Step1: Solve for \( h \)

Step2: Calculate \( \tan75^{\circ} \)

Step3: Calculate \( h \)

Answer: