InterviewSolution
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InterviewSolution
| 1. |
Am is perpendicular to bc tan b is 3/4 and tan c is 5/2 bc is 56 cm find l of am |
| Answer» In right\xa0{tex}\\triangle {/tex}AMB,\xa0tan B =\xa0{tex}\\frac { 3 } { 4 }{/tex}{tex}\\Rightarrow{/tex}\xa0{tex}\\frac { A M } { B M } = \\frac { 3 } { 4 }{/tex}{tex}\\Rightarrow{/tex}\xa04AM = 3BM {tex}\\Rightarrow{/tex}BM =\xa0{tex}\\frac { 4 } { 3 }{/tex}AM ...(i)In right\xa0{tex}\\triangle{/tex}AMC,tan C =\xa0{tex}\\frac { \\mathrm { AM } } { \\mathrm { MC } }{/tex}{tex}\\Rightarrow \\frac { 5 } { 12 } = \\frac { \\mathrm { AM } } { \\mathrm { MC } }{/tex}{tex}\\Rightarrow{/tex}\xa0MC =\xa0{tex}\\frac { 12 } { 5 }{/tex}\xa0AM ...(ii)Now, BM + MC = BC{tex}\\frac { 4 } { 3 }{/tex}AM +\xa0{tex}\\frac { 12 } { 5 }{/tex}AM = 56AM\xa0{tex}\\left( \\frac { 4 } { 3 } + \\frac { 12 } { 5 } \\right){/tex}\xa0= 56AM\xa0{tex}\\left( \\frac { 20 + 36 } { 15 } \\right){/tex}\xa0= 56{tex}\\Rightarrow{/tex}\xa0AM =\xa0{tex}\\frac { 56 \\times 15 } { 56 }{/tex}= 15 cm | |