Question

the acute angles of a right angled are in the ratio of 3:7 find the angle​

Answer 1

Answer:

3:7 =27degree :63 degree

Answer 2

Given :-

• Acute angles of a right angled triangle are in the ratio of 3:7.

To Find :-

• What are the acute angles of the given right angled triangle?

Solution :-

$\qquad$ ☀It's given that the acute angles of a right angled triangle are in the ratio of 3:7.

$\qquad$ ☀Let's assume the acute angles are 3x and 7x. Since, it is a right angled triangle, so the third angle will be 90°. Where sum of all the interior angles of a triangle is 180°.

$\qquad\small\underline{\pmb{\sf \:According \: to \: the \: question :-}}$

$\pink{\qquad\leadsto\quad \pmb {\mathfrak{ 90° + 3x + 7x = 180°}}}$

$\qquad\leadsto\quad \pmb {\mathfrak{ 90° + 10x = 180°}}$

$\qquad\leadsto\quad \pmb {\mathfrak{ 10x = 180° - 90°}}$

$\qquad\leadsto\quad \pmb {\mathfrak{ 10x = 90°}}$

$\qquad\leadsto\quad \pmb {\mathfrak{ x =\cancel{ \dfrac{90°}{ 10}}}}$

$\pink{\qquad\leadsto\quad \pmb {\mathfrak{ x = 9}}}$

Now, we'll find the acute angles.

$\qquad$ ☀First acute angle :

$\qquad$ $\Rightarrow$ 3x

$\qquad$ $\Rightarrow$ 3(9)°

$\qquad$ $\Rightarrow$ 27°

$\qquad$ ☀Second acute angle :

$\qquad$ $\Rightarrow$ 7x

$\qquad$ $\Rightarrow$ 7(9)°

$\qquad$ $\Rightarrow$ 63°

• The acute angles of the right angled triangle are 27° and 63°.

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