Question

the acute angle of a right traingle are in ratio of 4:5.find each of these angle​

Answer 1

Given: In a right angled triangle, the acute angles are in the ratio of 4 : 5.

❍ Let's say, that the angles be 4n and 5n.

$\underline{\bf{\dag} \:\frak{As\;we\;know\;that\: :}}$⠀

• ASP (Angle Sum ProPerty) of the triangle States that sum of all angles of a triangle is 180°. & the third angle of triangle will be 90°.

⠀

$:\implies\sf\quad 4n + 5n + 90^\circ = 180^\circ$

$:\implies\sf\quad 9n + 90^\circ = 180^\circ$

$:\implies\sf\quad 9n = 180^\circ - 90^\circ$

$:\implies\sf\quad 9n = 90^\circ$

$:\implies\sf\quad n = \cancel\dfrac{90^\circ}{9}$

$:\implies\quad{\pmb{\sf{n = 10^\circ}}}$

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⠀⠀

Therefore,

• 4n = 4(10) = 40
• 5n = 5(10) = 50

⠀

$\therefore{\underline{\sf{Hence,~ the~ angles~ of\; \triangle \;are\;\pmb{\sf{40^\circ}}\;and\;\pmb{\sf{50^\circ}} \; respectively.}}}$

Answer 2

As every , sum of 3 sides of angle in a triangle is 180°

and , Right angle = 90°

then ,

Sum of two acute angles = 180° - 90° = 90°

so , let each part of ratio be y

so ,

$\sf4y + 5y = 90°$

$\sf 9y = 90°$

$\bf y = \frac{90}{9} = 10°$

$\huge \red \dag \: \: \: \boxed{ \blue{ \sf y = 10°}}$

so , Finding the angles ,

4(10°) = 40°

5(10°) = 50°