Answer:
This is an Obtuse triangle.
Step-by-step explanation:
A Equilateral Triangle is a triangle where all sides are equal. Here all sides are different so it is not an Equilateral Triangle.
Isosceles triangle is a triangle that has 2 sides that are equal. Here all sides are different therefore this is not an Isosceles triangle.
A right angled triangle is a triangle whose sides satisfy the following equality.
Lets say A triangle has sides a, b and c. Where c is the highest value.
Then, [tex]a^{2} +b^{2} =c^{2}[/tex]
Lets substitute the values to the above equation to see whether it the triangle we are given satisfies the above equality,
[tex]7^{2} +15^{2}[/tex] = [tex]49+225[/tex]=[tex]274[/tex]
[tex]17^{2} =289[/tex]
Therefore, [tex]7^{2} +15^{2}[/tex] ≠[tex]17^{2}
So it is not a Right Angled Triangle.
If the sum of squares of the shorter sides is greater than the square of the longer side then it is an Acute angle if not it is an obtuse angle.
[tex]7^{2} +15^{2}[/tex] = [tex]274[/tex]≤[tex]17^{2} =289[/tex]
Therefore, This is an Obtuse triangle.
