Question

Arrange the three side
lengths in increasing
order.

Answer 1

Rest angle:-

• 180-(69+54)
• 180-123
• 57

Note that smaller side has smaller opposite angle

Hence the order is

• a<c<b

Answer 2

a < c < b

Explanation:

The sum of the interior angles of a triangle is 180°

Therefore, the measure of the missing angle (opposite side c) is:

180° - 69° - 54° = 57°

Relationship between sides and interior angles of any triangle:

• The shortest side is always opposite the smallest angle
• The longest side is always opposite the largest angle

Therefore, from inspection of the triangle:

• a is opposite the smaller angle of 54°
• c is opposite the angle of 57°
• b is opposite the largest angle of 69°

So the side lengths in increasing order are:

a < c < b