The angles in a triangle are in the ratio 1 : 2 : 3 - OCR - GCSE Maths - Question 8 - 2017 - Paper 1

To demonstrate that the triangle is a right-angled triangle, first, determine the angles based on the ratio given, which is 1 : 2 : 3.

Let the common ratio be represented as $x$. Therefore, the angles can be expressed as:

• First angle = $1x = x$
• Second angle = $2x = 2x$
• Third angle = $3x = 3x$

Since the sum of the angles in any triangle is $180^ ext{o}$, we can set up the equation:

$x + 2x + 3x = 180$

This simplifies to:

$6x = 180$

From this, solving for $x$ gives:

$x = 30$

Using this value, the individual angles are:

• First angle = $30^ ext{o}$
• Second angle = $60^ ext{o}$
• Third angle = $90^ ext{o}$

Since one of the angles is $90^ ext{o}$, we can conclude that it is a right-angled triangle.