Acute triangle
An acute triangle is a triangle in which all three angles are acute angles
An acute triangle is a triangle in which all three angles are acute angles. An acute angle is an angle that measures less than 90 degrees.
To understand an acute triangle better, let’s look at an example.
Suppose we have a triangle with sides of lengths 5, 6, and 7. We want to determine whether this triangle is acute.
To do this, we will use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In our triangle, let’s label the sides as follows: side a has length 5, side b has length 6, and side c (the hypotenuse) has length 7.
Now, let’s apply the Pythagorean theorem:
a^2 + b^2 = c^2
5^2 + 6^2 = 7^2
25 + 36 = 49
61 = 49 (a contradictory statement)
Since 61 is not equal to 49, we conclude that our triangle is not right-angled. And since it is not right-angled, it must be acute.
In summary, an acute triangle is a triangle in which all three angles are acute angles, with each angle measuring less than 90 degrees.
More Answers:
Understanding and Solving Problems related to Rhombuses: Properties, Area, Perimeter – A Comprehensive GuideProperties and Formulas of Squares in Mathematics: Perimeter, Area, and Diagonal Calculation
Pythagorean Theorem and Trigonometric Functions: Understanding Right Triangles and Solving Mathematical Problems