Solution:
(a) We are required to determine if a triangle can be formed from the lengths;
3, 8 , 10.
To determine this, all you have to do is use the Triangle Inequality Theorem, which states that the sum of two side lengths of a triangle is always greater than the third side.
Two shorter sides of the triangle are 3, 8.
The longest side = 10
Since 3 + 8 > 10. Hence, a triangle can be formed from the lengths
(b) To classify the triangle:
Judging from the lengths given, One of the angles of the triangle will give an obtuse angle. Reason being that the size of the length of a triangle is always proportional to the angle size.
Alternatively, we can conclude this by finding the angles of the triangle using cosine rule.
The angles of the triangle are shown in the picture below.
The angle facing side 10 is 124.2 degrees which is an obtuse angle. Thus,
The triangle is an obtuse angled triangle