Answer:
x=0.59 ft
Explanation:
First, determine the value of angle A.
[tex]\begin{gathered} m\angle A+m\angle B+m\angle C=180\degree \\ m\angle A+17\degree+118\degree=180\degree \\ m\angle A+135\degree=180\degree \\ m\angle A=180\degree-135\degree \\ m\angle A=45\degree \end{gathered}[/tex]
Next, applying the Law of Sines:
[tex]\begin{gathered} \frac{a}{\sin A}=\frac{b}{\sin B} \\ \frac{1.42}{\sin45\degree}=\frac{x}{\sin 17\degree} \end{gathered}[/tex]
Multiply both sides by sin 17°:
[tex]\begin{gathered} x=\sin 17\degree\times\frac{1.42}{\sin45\degree} \\ x=0.59ft \end{gathered}[/tex]
The value of the unknown is 0.59 ft. (correct to 2 d.p.)
