Question

please solve the question​

Answer 1

Question:

In a right angled triangle the acute angles are in the ratio of 3:7. Find the acute angles.

Answer:

27° and 63°

Step-by-step explanation:

Given that,

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

Let us assume the acute angles of a right angled triangle are in the ratio of 3:7 as 3x and 7x. Since, it is a right angled triangle, so the third angle will be 90°.

As we know that, sum of all the interior angles of a triangle is 180°. So,

$\longrightarrow$ 90° + 3x + 7x = 180°

$\longrightarrow$ 90° + 10x = 180°

$\longrightarrow$ 10x = 180° - 90°

$\longrightarrow$ 10x = 90°

$\longrightarrow$ x = 90° ÷ 10

$\longrightarrow$ x = 9

Now, we'll find the acute angles.

First acute angle :

$\longrightarrow$ 3x

$\longrightarrow$ 3(9)°

$\longrightarrow$ 27°

Second acute angle :

$\longrightarrow$ 7x

$\longrightarrow$ 7(9)°

$\longrightarrow$ 63°

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

Answer 2

$\huge\fbox\orange{QUE}{\colorbox{blue}{ST}}\fbox\green{ION}$

In a right angled triangle the acute angles are in the ratio 3 : 7. Find the acute angles.

$\huge{\underline{\mathtt{\red{A}\pink{N}\green{S}\blue{W}\purple{E}\orange{R}}}}$

$\sf\green{Given :}$

➣ The Acute Angles of a right angled triangle are in the ratio 3 : 7

$\sf\red{To \: Find :}$

➣ The First acute angle of a right angled triangle

➣ The Second Acute Angle of a right angled triangle

$\sf\pink{Solution :}$

➪ Let,the first acute angle = 3x

➪ Let,the second acute angle = 7x

➪ Since, the triangle is a right angled triangle then the third angle measure 90°

➪ Sum of all the interior angles of a triangle = 180°

⇒ 3x + 7x + 90° = 180°

⇒ 10x + 90° = 180°

⇒ 10x = 180° - 90°

⇒10x = 90°

⇒ x = $\cancel \frac{90}{10}$

⇒x = 9

First Acute Angle of a right angled triangle :—

⟼ First Acute Angle = 3x

⟼ First Acute Angle = 3 × 9

⟼ First Acute Angle = 27°

Second Acute Angle of a right angled triangle :-

⟼ Second Acute Angle = 7x

⟼ Second Acute Angle = 7 × 9

⟼ Second Acute Angle = 63°

➦$\sf\blue{So,\: the \:acute\: angles \:of \:the}$$\sf\blue{right\: angled\: triangle \:are \:27° \:and \:63°}$