What is the longest side of triangle ABC?
The two legs meet at a 90° angle and the hypotenuse is the longest side of the right triangle and is the side opposite the right angle.
Since your question specifies that A is the 90 degree angle, then BC would be the hypotenuse, and therefore the longest side.
How do you know which side of a triangle is the longest?
In a triangle: The shortest side is always opposite the smallest interior angle. The longest side is always opposite the largest interior angle.
Which is the longest side in the triangle ABC right angled at B?
AC is the longest side as the triangle is a right – angled triangle and the side opposite to the right angle of a right angled triangle is always called Hypotenuse and it is always the longest side.
Why is the longest side opposite the largest angle?
As you might guess, the largest angle will be opposite 18 because it is the longest side. Therefore, the angle measure in the middle will be opposite 13. Theorem: If one side of a triangle is longer than another side, then the angle opposite the longer side will be larger than the angle opposite the shorter side.
What is the shortest side of a right triangle?
The third side–the side opposite the right angle–is called the hypotenuse of the right triangle. The two shorter sides are usually called “legs.” This formula is called the Pythagorean Theorem in honor of Pythagoras.
Which triangle has maximum area?
Maximum Area Property of Equilateral Triangles. A particular case of the Isoperimetric Theorem tells us that among all triangles with the same perimeter, the equilateral one has the largest area.
Which side is the longest?
For a right angled triangle, the largest angle is 90° hence the longest side is the side opposite to this angle that is the hypotenuse. Hence, in a right angled triangle the longest side is the hypotenuse.
What is the relationship between the largest angle of a triangle and the side opposite it?
Relationship between sides and angles. In any triangle, the largest side and largest angle are opposite one another. In any triangle, the smallest side and smallest angle are opposite one another. In any triangle, the mid-sized side and mid-sized angle are opposite one another.
How do I find the third side of a triangle?
In particular, the Law of Cosines can be used to find the length of the third side of a triangle when you know the length of two sides and the angle in between. To use the Law of Sines to find a third side: 1. Identify angle C. It is the angle whose measure you know.
How do you list sides from shortest to longest?
To put the sides in order of longest to shortest, first find the largest angle — the longest side is opposite this angle. Then, find the second largest angle and the side opposite from it to find the next largest angle, and finally, the shortest side will be opposite the smallest angle.
Can a triangle have sides with the given lengths?
The sum of the lengths of any two sides of a triangle is greater than the length of the third side. Example 1: Check whether it is possible to have a triangle with the given side lengths. Add any two sides and see if it is greater than the other side.
What is a triangle with unequal sides?
A triangle is scalene if all of its three sides are different (in which case, the three angles are also different). If two of its sides are equal, a triangle is called isosceles. A triangle with all three equal sides is called equilateral.
How do you find the length of the short side of a triangle?
To find the length of a shorter side
- Sketch triangle.
- Mark hypotenuse.
- Write out pythagoras’ theorem for the triangle. (Hypotenuse)2 = (Shortest side)2 + (Other side)2
- Solve.
- Write out solution.
Are two sides of a right triangle equal?
The Pythagorean theorem states that: In any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).
What is the longest side of a triangle called?
hypotenuse
Photo in the article by “Wikimedia Commons” https://commons.wikimedia.org/wiki/File:Triangle_ABC_with_Sides_a_b_c_2.png