1. The lengths of the three sides of a triangle are given. Classify each triangle as acute, right, or obtuse.
NUMBERS: 30, 40, 50.
I'm confused by this question, could someone help/explain what it is asking.
How did you get this? where did the numbers come from and what formula did you use?
well, I happen to know that
3^2 + 4^2 = 9+16 = 5^2
so 30^2 + 40^2 = 50^2
so that is a right triangle.
Damon used the Pythagorean Theorem.
http://www.mathsisfun.com/pythagoras.html
Oh, Pythagoras !
http://www.mathsisfun.com/pythagoras.html
Certainly! This question is asking you to classify a triangle based on the lengths of its sides. In order to do this, you need to understand the definitions of acute, right, and obtuse triangles.
1. An acute triangle is a triangle where all three angles are less than 90 degrees.
2. A right triangle is a triangle that has one angle equal to 90 degrees (a right angle).
3. An obtuse triangle is a triangle where one angle is greater than 90 degrees.
To answer this question, you need to compare the given side lengths and determine the relationship between them. In this case, the side lengths are 30, 40, and 50. You can use the Pythagorean theorem (a^2 + b^2 = c^2) to determine if the triangle is right-angled or not.
By substituting the side lengths into the formula, you can find that:
30^2 + 40^2 = 900 + 1600 = 2500
So, 2500 is not equal to 50^2 (2500), which means it is not a right-angled triangle.
Now, let's check if it is an acute or obtuse triangle. To determine this, we need to compare the square of the longest side (50^2) to the sum of the squares of the remaining two sides (30^2 + 40^2).
If the square of the longest side is larger, it is an obtuse triangle. If it's smaller, it is an acute triangle. In this case, 50^2 is equal to 2500, but the sum of 30^2 (900) and 40^2 (1600) is equal to 2500 as well. This means that the triangle is neither acute nor obtuse—it is a degenerate triangle, where the three sides lie on the same line.
Therefore, the classification of the triangle with side lengths 30, 40, and 50 is degenerate.