We will draw a sketch to see the position of the cable
From the figure, we can use the tangent ratio to find the height
[tex]\frac{h}{42.7}=tan(29.6)[/tex]By using the cross-multiplication
[tex]\begin{gathered} h=42.7tan(29.6) \\ \\ h=24.3\text{ feet} \end{gathered}[/tex]a) The height of the pole is 24.3 feet to the nearest tenth
To find the length of the cable we will use the cosine ratio
[tex]cos(29.6)=\frac{42.7}{L}[/tex]Switch L and cos(29.6)
[tex]\begin{gathered} L=\frac{42.7}{cos(29.6)} \\ \\ L=49.1\text{ feet} \end{gathered}[/tex]b) The length of the cable is 49.1 feet to the nearest tenth