In triangle PQR angle Q is right triangle , PR = 7, PQ = 6 determine angle QPR and angle PRQ

In triangle PQR angle Q is right triangle , PR = 7, PQ = 6 determine a

1.	In triangle PQR angle Q is right triangle , PR = 7, PQ = 6 determine angle QPR and angle PRQ
Answer» In\xa0{tex}\\triangle{/tex}PQR{tex}\\sin ( \\angle \\mathrm { PRQ } ) = \\frac { \\mathrm { PQ } } { \\mathrm { PR } }{/tex}{tex}\\Rightarrow{/tex}\xa0{tex}\\sin ( \\angle \\mathrm { PRQ } ) = \\frac { 6 } { 12 } = \\frac { 1 } { 2 }{/tex}Also, sin 30°\xa0{tex}= \\frac { 1 } { 2 }{/tex}{tex}\\Rightarrow \\angle P R Q = 30 ^ { \\circ }{/tex}In right\xa0{tex}\\triangle{/tex}PQR,\xa0{tex}\\angle Q + \\angle R + \\angle P = 180 ^ { \\circ }{/tex}{tex}90 ^ { \\circ } + 30 ^ { \\circ } + \\angle P = 180 ^ { \\circ }{/tex}{tex}\\Rightarrow \\angle P = 60 ^ { \\circ }{/tex}{tex}\\therefore{/tex}\xa0{tex}\\angle \\mathbf { Q P R } = 60 ^ { \\circ } , \\angle \\mathbf { P R Q } = 30 ^ { \\circ }{/tex}