[tex]\bold{\huge{\green{\underline{ Solution}}}}[/tex]
[tex]\bold{\underline{ Given :- }}[/tex]
- We have given a right angled triangle whose values are m, n and 2
[tex]\bold{\underline{ To \: Find :- }}[/tex]
- We have to find the value of m and n
[tex]\bold{\underline{ Let's \: Begin :- }}[/tex]
In the given right angled triangle, we have
- Perpendicular height = n units
- Base = 2 units
- Hypotenuse = m units
Now, By using trigonometric ratios
[tex]\bold{\pink{ Sin Φ = }}{\bold{\pink{\frac{Perpendicular }{Hypotenuse}}}}[/tex]
[tex]\bold{\red{ Cos Φ = }}{\bold{\red{\frac{Base}{Hypotenuse }}}}[/tex]
[tex]\bold{\blue { tan Φ = }}{\bold{\blue{\frac{Perpendicular }{Base }}}}[/tex]
According to the question :-
[tex]\bold{ Cos \: 45° = }{\bold{\frac{2}{m}}}[/tex]
[tex]\bold{ 1/√2= }{\bold{\frac{2}{m}}}[/tex]
[tex]\bold{\red{ m = 2√2 \: units }}[/tex]
- We know that , Sum of Angles of triangle is 180° .
Therefore,
Let the unknown angle be x
[tex]\sf{ 45° + x + 90° = 180° }[/tex]
[tex]\sf{ x = 180° - 135 ° }[/tex]
[tex]\sf{ x = 45° }[/tex]
Now,
[tex]\bold{ Cos \: x° = }{\bold{\frac{n}{2√2}}}[/tex]
[tex]\bold{ Cos \: 45° = }{\bold{\frac{n}{2√2}}}[/tex]
[tex]\bold{ 1/√2= }{\bold{\frac{n}{2√2}}}[/tex]
[tex]\bold { n = 2√2/√2 }[/tex]
[tex]\bold{\red{ n = 2\: units }}[/tex]
Thus, The value of m = 2√2 and n = 2
[tex]\sf{\blue{ Hence, \: option \: D \: is \: Correct }}[/tex]
