Question

The acute angles of a right triangle are in the ratio 4:5. Find each of these angles.​

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°.

⠀

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

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

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

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

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

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

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Therefore,

4n = 4(10) = 40

5n = 5(10) = 50

⠀

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