Concepts. The longest side in a triangle is opposite the largest angle, and the shortest side is opposite the smallest angle. Triangle Inequality: In any triangle, the sum of the lengths of any two sides is greater than the length of the third side. Pythagorean Theorem: In a right triangle with hypotenuse c, a2+b2=c2.
How do you know that a certain side is the longest side in right triangle?
In a right triangle, the hypotenuse is the longest side, an “opposite” side is the one across from a given angle, and an “adjacent” side is next to a given angle. … The hypotenuse of a right triangle is always the side opposite the right angle. It is the longest side in a right triangle.
How do you find the long side of a triangle?
Hypotenuse calculator
The hypotenuse is opposite the right angle and can be solved by using the Pythagorean theorem. In a right triangle with cathetus a and b and with hypotenuse c , Pythagoras’ theorem states that: a² + b² = c² . To solve for c , take the square root of both sides to get c = √(b²+a²) .
What is the shortest side of a right triangle?
In any triangle, the longest side is opposite the largest angle, and the shortest side is opposite the smallest angle. Thus, in a right triangle, the hypotenuse is always the longest side.
Which side of triangle God is the shortest?
In such a triangle, the shortest side is always opposite the smallest angle. (These are shown in bold color above) Similarly, the longest side is opposite the largest angle. In the figure above, drag any vertex of the triangle and see that whichever side is the shortest, the opposite angle is also the smallest.
Does 9 12 and 15 make a right triangle?
The three sides 9 in, 12 in, and 15 in do represent a right triangle. Since the square of the hypotenuse is equal to the sum of the squares of the other two sides, this is a right triangle.
How do you know if it is a right triangle?
A right triangle is a triangle in which one of the angles is a 90∘ angle. … A triangle can be determined to be a right triangle if the side lengths are known. If the lengths satisfy the Pythagorean Theorem (a2+b2=c2) then it is a right triangle.
What is the rule for side lengths of a triangle?
Triangle Inequality Theorem. The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
What is the possible lengths of the third side?
Explanation: The sum of the lengths of 2 sides of a triangle must be greater than—but not equal to—the length of the third side. Further, the third side must be longer than the difference between the greater and the lesser of the other two sides; therefore, 20 is the only possible answer.
How do you find the third side of a triangle given two sides?
To use the Law of Sines to find a third side:
- Identify angle C. It is the angle whose measure you know.
- Identify a and b as the sides that are not across from angle C.
- Substitute the values into the Law of Cosines.
- Solve the equation for the missing side.
How do you find the minimum and maximum length of the third side of a triangle?
By the Triangle Inequality Theorem, the sum of lengths of any two sides of a triangle is greater than the length of the third side. So, The minimum would be 6 and the maximum would be 20.
Is Side A always longer than Side B in a right triangle?
2 Answers. Side A and B does not matter when your trying to apply this to the pythagorean theorem but side C must always be the hypotenuse. The hypotenuse is always the triangle’s longest side. It is opposite the right angle.
Are 2 sides equal in a right triangle?
A right triangle has one angle equal to 90 degrees. A right triangle can also be an isosceles triangle–which means that it has two sides that are equal. A right isosceles triangle has a 90-degree angle and two 45-degree angles.
What are the side lengths of a 30 60 90?
A 30-60-90 triangle is a special right triangle whose angles are 30º, 60º, and 90º. The triangle is special because its side lengths are always in the ratio of 1: √3:2. Any triangle of the form 30-60-90 can be solved without applying long-step methods such as the Pythagorean Theorem and trigonometric functions.