Výpočet trojúhelníků
Vypočítej zbývající strany a úhly trojúhelníků:
\( UPS \), kde \( \left|UP\right|=3\ cm,\:\left|PS\right|=5\ cm,\:\left|\measuredangle SUP\right|=43\degree34 \)'
\( \left |SU \right|^{2} = \left |UP \right |^{2} + \left |PS \right |^{2} − 2\left |UP \right| \left |PS \right|\textrm{sin}\ \left |\measuredangle UPS \right| \)
\( \left |SU \right| = \sqrt {\left |UP \right |^{2} + \left |PS \right |^{2} − 2\left |UP \right| \left |PS \right|\textrm{sin}\ \left |\measuredangle UPS \right|} \)
\( \left |SU \right| = \sqrt{3^{2} + 5^{2} − 2 \cdot 3 \cdot 5 \cdot (\textrm{sin}\ 112°) } \)
\( \left |SU \right| \doteq 6,7\ cm \)
\( \left |SU \right|^{2} = \left |UP \right |^{2} + \left |PS \right |^{2} − 2\left |UP \right| \left |PS \right|\textrm{cos}\ \left |\measuredangle UPS \right| \)
\( \left |SU \right| = \sqrt {\left |UP \right |^{2} + \left |PS \right |^{2} − 2\left |UP \right| \left |PS \right|\textrm{cos}\ \left |\measuredangle UPS \right|} \)
\( \left |SU \right| = \sqrt{3^{2} + 5^{2} − 2 \cdot 3 \cdot 5 \cdot (\textrm{cos}\ 112°) } \)
\( \left |SU \right| \doteq 6,7\ cm \)
\( \left |SU \right|^{2} = \left |UP \right |^{2} + \left |PS \right |^{2} − 2\left |UP \right| \left |PS \right|\textrm{cos}\ \left |\measuredangle SUP \right| \)
\( \left |SU \right| = \sqrt {\left |UP \right |^{2} + \left |PS \right |^{2} − 2\left |UP \right| \left |PS \right|\textrm{cos}\ \left |\measuredangle SUP \right|} \)
\( \left |SU \right| = \sqrt{3^{2} + 5^{2} − 2 \cdot 3 \cdot 5 \cdot (\textrm{cos}\ 43°34') } \)
\( \left |SU \right| \doteq 6,7\ cm \)
\( \left |SU \right|^{2} = \left |UP \right |^{2} + \left |PS \right |^{2} + 2\left |UP \right| \left |PS \right|\textrm{cos}\ \left |\measuredangle UPS \right| \)
\( \left |SU \right| = \sqrt {\left |UP \right |^{2} + \left |PS \right |^{2} + 2\left |UP \right| \left |PS \right|\textrm{cos}\ \left |\measuredangle UPS \right|} \)
\( \left |SU \right| = \sqrt{3^{2} + 5^{2} + 2 \cdot 3 \cdot 5 \cdot (\textrm{cos}\ 112°) } \)
\( \left |SU \right| \doteq 6,7\ cm \)