A) \[\frac{25}{2}\sqrt{3}c{{m}^{2}}\]
B) \[25\,\,c{{m}^{2}}\]
C) \[25\sqrt{3}c{{m}^{2}}\]
D) \[\frac{75}{2}c{{m}^{2}}\]
Correct Answer: A
Solution :
From\[\Delta ABC\] \[\sin {{30}^{o}}=\frac{AB}{AC}\Rightarrow \frac{1}{2}=\frac{AB}{AC}\] \[\Rightarrow \] \[AB=\frac{1}{2}AC=\frac{1}{2}\times 10=5\,\,cm\] \[\therefore \] \[BC=\sqrt{A{{C}^{2}}-A{{B}^{2}}}=\sqrt{{{10}^{2}}-{{5}^{2}}}\] \[=\sqrt{100-25}=\sqrt{75}=5\sqrt{3}cm\] \[\therefore \]Area of\[\Delta ABC\] \[=\frac{1}{2}\times AB\times BC\] \[=\frac{1}{2}\times 5\times 5\sqrt{3}=\frac{25\sqrt{3}}{2}c{{m}^{2}}\]You need to login to perform this action.
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