Answer:
23.1 ft
Step-by-step explanation:
Consider right triangle LMN. In this triangle,
[tex]m\angle M=55^{\circ}\\ \\LN=16\ ft[/tex]
By sine definition,
[tex]\sin \angle M=\dfrac{\text{Opposite leg}}{\text{Hypotenuse}}=\dfrac{LN}{LM}=\dfrac{16}{LM}\\ \\LM=\dfrac{16}{\sin 55^{\circ}}[/tex]
In triangle KLM, by sine theorem,
[tex]\dfrac{LM}{\sin \angle K}=2R,[/tex]
where R is the radius of circumscribed circle.
Therefore,
[tex]R=\dfrac{1}{2}\cdot \dfrac{\dfrac{16}{\sin 55^{\circ}}}{\sin 25^{\circ}}=\dfrac{8}{\sin 55^{\circ}\cdot \sin 25^{\circ}}\approx 23.1\ ft[/tex]
