10.8.0: Exercises
- Page ID
- 171799
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Use the Pythagorean theorem to answer the following exercises. Let \(a\) and \(b\) represent two legs of a right triangle, and let \(c\) represent the hypotenuse. Find the lengths of the missing sides.
If \(b = 25\) and \(c = 65{\text{ ft}}\), find \(a\).
If \(a = 18{\text{ ft}}\) and \(c = 30{\text{ ft}}\), find \(b\).
If \(b = 12{\text{ cm}}\) and \(c = 15{\text{ cm}}\), find \(a\).
Refer to the \({30^ \circ} {\text{-}} {60^ \circ } {\text{-}} {90^ \circ }\) triangle shown for the following exercises.
If \(b = 10\), find \(c\) and \(a\)
If \(a = 2\sqrt 3{\text{ ft}}\), find \(b\) and \(c\).
If \(b = 7{\text{ cm}}\), find \(a\) and \(c\)
If \(c = \sqrt 3 \), find \(a\) and \(b\).
If \(c = 8\sqrt 3 \), find \(a\) and \(b\)
Refer to the \({45^ \circ }{\text{-}}{45^ \circ }{\text{-}}{90^ \circ }\) triangle shown in the following exercises.
If \(a = 15{\text{ cm}}\), find \(b\).
If \(a = 3\sqrt {2}{\text{ ft}}\), find \(a\).
If \(a = 4\sqrt 5{\text{ cm}}\), find \(b\).
If \(a = 10{\text{ ft}}\), find \(b\).
If \(b = \frac
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In the provided figure given \(\alpha = {10^ \circ }\), find the unknown sides and angles.
Evaluate the expressions in the following exercises.
\({\sin ^{ - 1}}\left( {\frac{2}{5}} \right)\)
\({\tan ^{ - 1}}(5.68)\)
\({\cos ^{ - 1}}\left( {\frac{1}{9}} \right)\)
Use the figure shown to solve for all missing sides and angles given \(a = 6,\,b = 8\).
Use the figure shown to solve for all missing sides and angles given \(\alpha = {16^ \circ },\,c = 20\).
