10)
Given data:
The given height of the tree branch is h=15.4 ft.
The length of the ladder is l=18 ft.
The expression for the angle made by the ladder with horizontal is,
[tex]\begin{gathered} \sin \theta=\frac{h}{l} \\ \sin \theta=\frac{15.4}{18} \\ \theta=58.82^{\circ} \end{gathered}[/tex]
Thus, the angle made by the ladder with horizontal is 58.82 degrees.
11)
Given data:
The given triangle.
The tanB is,
[tex]\begin{gathered} \sin B=\frac{5}{12} \\ B=24.62^{\circ} \end{gathered}[/tex]
The tanB is,
[tex]\begin{gathered} \tan B=\tan 24.62^{\circ} \\ =0.458 \end{gathered}[/tex]
Thus, the value of tanB is 0.458.
