A bridge across a river angle of 45 degree with the river bank

1.	A bridge across a river angle of 45 degree with the river bank
Answer» Given that a bridge across a river makes an angle of 45o with the river bank as shown in Fig. If the length of the bridge across the river is 150 m, we have to find the width of the river.In right triangle ABC, we have {tex} \\sin 45 ^ { \\circ } = \\frac { B C } { A C }{/tex}{tex}\\Rightarrow \\quad \\frac { 1 } { \\sqrt { 2 } } = \\frac { B C } { 150 }{/tex}{tex}\\Rightarrow \\quad B C = \\frac { 150 } { \\sqrt { 2 } }{/tex}( rationalization by √2){tex}\\Rightarrow \\quad B C = 75 \\sqrt { 2 } \\mathrm { m }{/tex}Hence, the width of the river is\xa0{tex}75 \\sqrt { 2 }{/tex} metres.

Discussion