Question

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

Answer 1

Answer:

40° & 50°

Step-by-step explanation:

Since it is a Right Triangle

Therefore One Angle Must be 90°

Let the common ratio be X

Therefore angles are 4x , 5x , 90°

Since we know that the sum of all the angles in a triangle is 180° { Angle Sum Property }

Therefore ,

4x + 5x + 90° = 180°

4x + 5x = 180° - 90°

4x + 5x = 90°

9x = 90°

x = (90/9)°

X = 10°

Since the angles are 4x and 5x

Therefore ,

4x = 4(10°) = 40°

5x = 5(10°) = 50°

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Answer 2

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

⠀

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