Question

The difference between two acute angles of a right angled triangle is 7π^c/30

Find the angles of the triangle in degree​

Answer 1

$\bf \large \star Question :-$

• The difference between two acute angles of a right angled triangle is 7π/30

To find : The angles of the triangle in degree.

$\bf\huge\fbox{Answer :-}$

$\bf \small\text{Consider \:the \: \:following - }$

❒ Let's assume that x and y are the acute angle of triangle in degree.

$\bf\large \star Step \: by \: step \: \: Explanation :-$

$\large \bf \green\bigstar \: \: \red{ \underbrace{ \underline{Here}}}$

$\longmapsto \sf\:x -y = \frac{ {7\pi}^{c} }{30} = \sf \purple( \frac{7\pi}{30} \times \frac{180}{\pi} {)}^{°} }$

$\bf{\longmapsto = {42}^{°} }$

$\large \bf \red\bigstar \: \: \pink{ \underbrace{ \underline{so}}}$

$\pink{ \large :\longmapsto  \underline {\boxed{{\bf x - y = {42}^{°} } }}} \: \: (1)$

$\bf \large \dag We \: Know \: that :$

☞The triangle is right angled

$\green\dashrightarrow\underline{\underline{\sf  \red{x + y = {90}^{°} }} } \: \: \: (2)$

$\large \bf \red\bigstar \: \: \orange{ \underbrace{ \underline{now}}}$

●Add the both equation (1) and (2)

$\large \bf \red\bigstar \: \: \blue{ \underbrace{ \underline{we \: get}}}$

$:\longmapsto \rm \: x - y + x + y \\ \\ :\longmapsto 4 {2}^{°} + {90}^{°}\\\\ :\longmapsto \sf2x = {132}^{°}\\\\ :\longmapsto {66}^{°}$

$\bf{Place \: this \: in \: equation \: \: (1)}$

$\longmapsto \rm {66}^{°} - y = {42}^{°} \\\\ \longmapsto \sf{66}^{°} - {42}^{°} = y \\\\\longmapsto \sf{y = {24}^{°} }$

$\huge\underline{\green{\underline{\frak{\pmb{\text Therefore}}}}}$

✧ The angle of triangle are :

ミ66°

ミ90°

ミ24°

• @Okhey