9th Class
Mathematics
Geometry
Question Bank
Geometry
question_answer
Two beams of length \[{{l}_{1}}\] and \[{{l}_{2}}\] are leaning on opposite sides of a thin vertical wall meeting at the same point on the wall and making angles \[30{}^\circ \]and \[60{}^\circ \] with it respectively. Then \[{{l}_{2}}\] is equal to
A)\[\frac{{{l}_{1}}}{2}\]
B)\[2{{l}_{1}}\]
C)\[{{l}_{1}}\sqrt{2}\]
D)\[{{l}_{1}}\sqrt{3}\]
Correct Answer:
D
Solution :
Let OW be the wall. From \[\Delta \,AOW,\,\,\,x={{l}_{1}}\,\cos {{30}^{o}}=\frac{\sqrt{3}{{l}_{1}}}{2}\] From \[\Delta \,BOW,\] \[x={{l}_{2}}\,\cos \,{{60}^{o}}=\frac{{{l}_{2}}}{2}\] \[\therefore \] \[\frac{{{l}_{2}}}{2}=\frac{\sqrt{3}}{2}{{l}_{1}}\] or \[{{l}_{2}}=\sqrt{3}\,{{l}_{1}}\]