Question

Hey guys can anyone help me find the missing side length pls and ty

Answer 1

$\bold{\huge{\green{\underline{ Solution}}}}$

$\bold{\underline{ Given :- }}$

• We have given a right angled triangle whose values are m, n and 2

$\bold{\underline{ To \: Find :- }}$

• We have to find the value of m and n

$\bold{\underline{ Let's \: Begin :- }}$

In the given right angled triangle, we have

• Perpendicular height = n units
• Base = 2 units
• Hypotenuse = m units

Now, By using trigonometric ratios

$\bold{\pink{ Sin Φ = }}{\bold{\pink{\frac{Perpendicular }{Hypotenuse}}}}$

$\bold{\red{ Cos Φ = }}{\bold{\red{\frac{Base}{Hypotenuse }}}}$

$\bold{\blue { tan Φ = }}{\bold{\blue{\frac{Perpendicular }{Base }}}}$

According to the question :-

$\bold{ Cos \: 45° = }{\bold{\frac{2}{m}}}$

$\bold{ 1/√2= }{\bold{\frac{2}{m}}}$

$\bold{\red{ m = 2√2 \: units }}$

• We know that , Sum of Angles of triangle is 180° .

Therefore,

Let the unknown angle be x

$\sf{ 45° + x + 90° = 180° }$

$\sf{ x = 180° - 135 ° }$

$\sf{ x = 45° }$

Now,

$\bold{ Cos \: x° = }{\bold{\frac{n}{2√2}}}$

$\bold{ Cos \: 45° = }{\bold{\frac{n}{2√2}}}$

$\bold{ 1/√2= }{\bold{\frac{n}{2√2}}}$

$\bold { n = 2√2/√2 }$

$\bold{\red{ n = 2\: units }}$

Thus, The value of m = 2√2 and n = 2

$\sf{\blue{ Hence, \: option \: D \: is \: Correct }}$

Answer 2

Sense you have your answer already….

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