Classify the Triangle as Acute, Obtuse or Right. 5, 7, 10
To classify a triangle as acute, obtuse, or right, we need to compare the square of the lengths of the sides. Let's denote the sides of the triangle as follows:
Side a = 5
Side b = 7
Side c = 10
We need to determine if a^2 + b^2 > c^2, a^2 + b^2 < c^2, or a^2 + b^2 = c^2.
Using the given side lengths, let's substitute them into the formula:
5^2 + 7^2 = 25 + 49 = 74.
10^2 = 100.
Since 74 is less than 100, we can conclude that a^2 + b^2 < c^2. Therefore, the triangle is an obtuse triangle.
To classify a triangle as acute, obtuse, or right, we need to determine the relationship between its side lengths.
Step 1: Identify the longest side (also known as the hypotenuse if it is a right triangle) among the three given sides.
From the side lengths you provided, the longest side is 10.
Step 2: Apply the Pythagorean theorem to find out if the triangle is right-angled.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
If we square the lengths of the two shorter sides and add them together, we have:
5^2 + 7^2 = 25 + 49 = 74.
Step 3: Compare the sum of squares to the square of the hypotenuse.
- If the sum of squares is greater than the square of the hypotenuse, the triangle is obtuse.
- If the sum of squares is less than the square of the hypotenuse, the triangle is acute.
- If the sum of squares is equal to the square of the hypotenuse, the triangle is right-angled.
In this case, 74 is less than 10^2 (which is 100). Therefore, since 74 < 100, we can conclude that the triangle with side lengths 5, 7, and 10 is an acute triangle.
If the sides are 5,7,10 then since
5^2 + 7^2 < 10^2
there is no obtuse angle. And that also means there is no right angle.