(Solved): \( \vec{R} \) is a vector with length \( R \). Its angle relative the \( x \) and \( y \) axes are ...

\( \vec{R} \) is a vector with length \( R \). Its angle relative the \( x \) and \( y \) axes are \( \theta \) and \( \phi \), respectively. The \( x \) and \( y \) components are \( -D \) and \( H \), respectively. Based on the diagram at the right, what are the following expressions? Note any expressions that are similar. \( \left(\theta+\phi=90^{\circ}\right) \) 26. \( \mathrm{H} \) in terms of \( \mathrm{R}, \theta: \mathrm{H}= \) 27. \( \mathrm{H} \) in terms of \( \mathrm{R}, \phi: \mathrm{H}= \) 28. \( D \) in terms of \( R, \theta: D= \) 29. \( D \) in terms of \( R, \phi: D= \) 30. In terms of \( \mathrm{H} \) and \( \phi, \mathrm{R}= \) 31. What is \( R \) in terms of \( D \) and \( H \) ?