JEE Main & Advanced
JEE Main Paper (Held On 10-Jan-2019 Morning)
question_answer
Consider a triangular plot ABC with sides\[AB=7\,m\], \[BC=5\,m\] and\[CA=6\,m\]. A vertical lamp-post at the mid-point D of AC subtends an angle \[30{}^\circ \] at B. The height (in m) of the lamp-post is-
[JEE Main Online Paper (Held On 10-Jan-2019 Morning]
A)\[2\sqrt{21}\]
B)\[\frac{3}{2}\sqrt{21}\]
C)\[7\sqrt{3}\]
D) \[\frac{2}{3}\sqrt{21}\]
Correct Answer:
D
Solution :
Median \[{{m}_{B}}=\frac{1}{2}\sqrt{2{{a}^{2}}+2{{c}^{2}}-{{b}^{2}}}\]= \[=\,\,\frac{1}{2}\sqrt{2(49)+2(25)-36}\,=\,\sqrt{28}\] \[\tan \,30{}^\circ \,=\,\frac{h}{BD}\,=\,\frac{1}{\sqrt{3}}\] \[\Rightarrow \,\,h=\,\frac{\sqrt{28}}{\sqrt{3}}\,=\,\frac{2\sqrt{21}}{3}\,cm\]