Answer
$$\begin{aligned} \tan \theta &=0.39887 \end{aligned}$$
Work Step by Step
$\begin{aligned} A &=(0.150)(0.006)=0.9 \times 10^{-3} \mathrm{m}^{2} \\ \sigma_{x} &=\frac{P}{A}=\frac{200 \times 10^{3}}{0.9 \times 10^{-3}}=222.22 \times 10^{6} \mathrm{Pa} \\ \varepsilon_{x} &=\frac{\sigma_{x}}{E}=\frac{222.22 \times 10^{6}}{105 \times 10^{9}}=2.1164 \times 10^{-3} \\ \varepsilon_{y} &=-08_{x}=-(0.34)\left(2.1164 \times 10^{-3}\right) \\ &=-0.71958 \times 10^{-3} \end{aligned}$
$\begin{aligned} \tan \theta &=\frac{4\left(1+\varepsilon_{y}\right)}{10\left(1+\varepsilon_{x}\right)} \\ &=\frac{4\left(1-0.71958 \times 10^{-3}\right)}{10\left(1+2.1164 \times 10^{-3}\right)} \\ &=0.39887 \end{aligned}$
