جواب تمرین صفحه 34 درس 2 ریاضی دهم (مثلثات)

\(\tan {\mkern 1mu} \theta = \frac{h}{3} = \frac{{1/5}}{{0/5}} = 3 \Rightarrow h = 9\) متر

\(\begin{array}{l}\left. {\begin{array}{*{20}{l}}\begin{array}{l}B = {B_1} + {B_2} = 120^\circ \\ \Rightarrow {B_1} = {B_2} = 60^\circ \end{array}\\\begin{array}{l}\\BH = \frac{1}{2}AB = \frac{3}{2}\end{array}\\\begin{array}{l}\\\tan {\mkern 1mu} {B_1} = \frac{{OH}}{{BH}} \Rightarrow OH = BH \times \tan {\mkern 1mu} 60^\circ \\ = \frac{3}{2} \times \sqrt 3 = \frac{{3\sqrt 3 }}{2}\end{array}\\\begin{array}{l}\\{S_{A\mathop B\limits^\Delta C}} = \frac{1}{2} \times AB \times OH\\ = \frac{1}{2} \times 3 \times \frac{{3\sqrt 3 }}{2} = \frac{{9\sqrt 3 }}{4}\end{array}\end{array}\;} \right\}\\\\ \Rightarrow S = 6 \times {S_{A\mathop B\limits^\Delta C}} = \frac{{27\sqrt 3 }}{2}\end{array}\)

\(\begin{array}{l}\tan \,O = \frac{{AH}}{{OA}}\\\\ \Rightarrow OA = \frac{{AH}}{{\tan 13^\circ }} \simeq \frac{2}{{0/23}} \simeq 8/695\,Km\end{array}\)

\(\begin{array}{l}{S_{A\mathop B\limits^\Delta C}} = \frac{1}{2} \times AH \times BC\\\\\sin B = \frac{{AH}}{{AB}} \Rightarrow AH = AB \times \sin 75^\circ \\\\ = 3 \times 0/96 = 2/88\\\\{S_{A\mathop B\limits^\Delta C}} = \frac{1}{2} \times 2/88 \times 5 = 7/2\end{array}\)

\(\begin{array}{l}{S_{A\mathop B\limits^\Delta C}} = \frac{1}{2} \times BH \times AC\\\\\sin {\mkern 1mu} A = \frac{{BH}}{{AB}} \Rightarrow BH = AB \times \sin {\mkern 1mu} 30^\circ \\\\ = 3 \times \frac{1}{2} = \frac{3}{2}\\\\\cos {\mkern 1mu} A = \cos {\mkern 1mu} C = \frac{{AH}}{{AB}} = \frac{{HC}}{{BC}}\\\\ \Rightarrow AH = HC = 3 \times \cos {\mkern 1mu} 30^\circ = \frac{{3\sqrt 3 }}{2}\\\\AC = AH + HC = 3\sqrt 3 \\\\{S_{A\mathop B\limits^\Delta C}} = \frac{1}{2} \times \frac{3}{2} \times 3\sqrt 3 = \frac{{9\sqrt 3 }}{4}\end{array}\)