A) \[\frac{17}{5}\,m.\]
B) \[\frac{8}{5}\,m.\]
C) \[\frac{17}{10}\,m.\]
D) \[\frac{16}{5}\,m.\]
Correct Answer: D
Solution :
Height of tree \[AB=10\text{ }m.\] So, \[AD=CD=(10-h)\,m.\] In \[\Delta \,DBC\], \[\sin \theta =\frac{h}{10-h}\] .?..(i) \[\cos \theta =\frac{6}{10-h}\] ??(ii) From equation (i) and (ii)- \[{{\sin }^{2}}\theta +{{\cos }^{2}}\theta ={{\left( \frac{h}{10-h} \right)}^{2}}+{{\left( \frac{6}{10-h} \right)}^{2}}\] \[{{(10-h)}^{2}}={{h}^{2}}+36\] \[{{h}^{2}}+100-20h={{h}^{2}}+36\,\,\,\Rightarrow \,\,20h=64\] \[\therefore \,\,\,h=\frac{16}{5}\,m.\] \[\therefore \] Height at which the tree is broken \[=\,\,\,\,\,\underline{\frac{\mathbf{16}}{\mathbf{5}}\,\mathbf{m}}\]You need to login to perform this action.
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