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

Correct Question :-

The difference between two acute angles of right angle triangle is 7π/30. Find the angle of the triangle in degree.

Let :-

• The two acute angle be x and y
• The angle at right angled be z

Given :-

• The difference between two angles = 7π/30
• One the angle at right angled = 90°

To Find :-

• The angles of right angle triangle = ?

Solution :-

• To calculate the angles of triangle at first we have to set up equation. Then calculate the angles of triangle by applying sum angles property of triangle.

Difference between its acute angle = 7π/30

⇢ ∠x - ∠y = 7π/30 -------(i)

⇢ ∠x = 7π/30 + ∠y

Sum of angles of triangle = 180

⇢∠x + ∠y + ∠z = 180--------(ii)

• Putting values here :-] π = 180°

⇢ 7× 180/30 + ∠y + ∠y + 90 = 180

⇢ 7 × 6 + 2∠y + 90 = 180

⇢ 2∠y + 42 + 90 = 180

⇢ 2∠y = 180 - 42 - 90

⇢ 2∠y = 180 - 132

⇢ 2∠y = 48°

⇢ ∠y = 24°

• Putting the value ⇢ ∠y = 24° in eq (i)

⇢ ∠x - ∠y = 7π/30

⇢ ∠x - 24 = 7 × 180/30

⇢ ∠x = 7 × 6 + 24

⇢ ∠x = 42 + 24

⇢ ∠x = 66°

Hence the required angles of triangle are :-

⇢ ∠x = 66°. ⇢ ∠y = 24°. ⇢ ∠z = 90°

Answer 2

$\bf \large \dag Question :-$

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

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.

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

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

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

$\bf{\longmapsto = {42}^{°} }$

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

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

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

✧ The triangle is right angled

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

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

✧ Add the both equation (1) and (2)

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

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

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

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

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

✧ The angle of triangle are

• ✧66°
• ✧90°
• ✧24°

$\bf{ANSWER \: by }$

$\bf \red{AYUSH \: kings }$