Consider the following diagram,
Consider the side 212 feet side makes an angle as denoted in the figure.
Consider that both the triangle have the same base length,
[tex]180\sin (\varnothing+22)=212\sin (\varnothing)\Rightarrow\frac{\sin (\varnothing+22)}{\sin (\varnothing)}=\frac{212}{180}=\frac{53}{45}[/tex]
Solve the expression further,
[tex]\frac{\sin\varnothing.\cos22^{\circ}+\cos\varnothing.\sin22^{\circ}}{\sin\varnothing}=\frac{53}{45}\Rightarrow0.927^{}+\cot \varnothing.(0.3746)=\frac{53}{45}[/tex][tex]0.3746\cot \varnothing=0.251\Rightarrow\cot \varnothing=0.66945\Rightarrow\varnothing\approx56.2^{\circ}[/tex]
Now, the height of the statue is calculated as,
[tex]h=b.\cos \varnothing-a.\cos (\theta+\varnothing)=212.\cos 56.2-180.\cos (22+56.2)=154.744[/tex]
Thus, the height of the statue is approximately 154.744 feet.
