Question

If three angles of a triangle are in the ratio 3:7:10, show that triangle is right angled

Answer 1

Answer:

Yes, it's a right angled triangle.

Explanation:

Given ratio of three sides of a triangle is 3 : 7 : 10

Let's say the common ratio as x

Then, the side will be, 3x, 7, and 10x

We know that,

A right angled triangle is a triangle in which a right angle is formed i.e., 90°

According to the angle sum property,

→ 3x + 7x + 10x = 180°

→ 20x = 180°

→ x = 180/20

→ x = 9

Hence, the angle will be:

• 3x = 3(9) = 27°
• 7x = 7(9) = 63°
• 10x = 10(9) = 90°

Since,

One of the angle is 90°.

Hence, proved that the triangle is a right angled triangle.

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Angle sum property:

The sum of all angles in a triangle is 180° and known as angle sum property of a triangle.

Answer 2

Given :-

• Three angles of a triangle in ratio 3 : 7 : 10

To Prove :-

• The triangle is a right angled triangle

We know that :-

If an angle in a triangle measures 90°, then it is referred as a right angled triangle.

Proof :-

Lets take x as the common ratio

Therefore,

=> 3 = 3x

=> 7 = 7x

=> 10 = 10x

Using the angle sum property of a Triangle,

$\sf \leadsto3x + 7x + 10x = 180° \\ \sf \leadsto \: 20x = 180° \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf \leadsto \: x = \frac{180}{20} = 9° \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Therefore,

$\sf \rightarrow3x = 3 \times 9 = 27° \: \: \: \: \\ \sf \rightarrow7x = 7 \times 9 = 63° \: \: \: \: \\ \sf \rightarrow10x = 10 \times 9 = 90°$

Since, one of the angle measures 90°

Therefore, it is a right angled triangle.

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