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When do three side lengths measures form a triangle?
Three side lengths can form a triangle if they satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides must be greater than the length of the third side. This must hold true for all three combinations of the side lengths. For example, if the side lengths are (a), (b), and (c), then (a + b > c), (a + c > b), and (b + c > a) must all be true. If any of these conditions are not met, the side lengths cannot form a triangle.
How do you find out if a triangle is acute obtuse or a right triangle by the side lengths?
To determine if a triangle is acute, obtuse, or right based on its side lengths, you can use the Pythagorean theorem. For a triangle with sides (a), (b), and (c) (where (c) is the longest side), if (a^2 + b^2 = c^2), the triangle is right. If (a^2 + b^2 > c^2), it is acute, and if (a^2 + b^2 < c^2), it is obtuse.
How do you find the area and perimeter of a triangle?
Area:A=1/2bhA=Area b=Base h=HeightPerimeter:P=a+b+cP=Perimeter a,b,c=side lengths of the triangle
What is one way to find the missing side length?
One way to find a missing side length of a triangle is to use the Pythagorean theorem, which 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 (a² + b² = c²). If you know the lengths of two sides, you can rearrange the formula to solve for the missing side. For example, if you have the lengths of the two legs (a and b), you can find the hypotenuse (c) by calculating c = √(a² + b²).
How do you find the side length of a right triangle if you have two side lengths?
To find the length of the third side of a right triangle when you have the lengths of the two sides, you can use the Pythagorean theorem. If you know the lengths of the two legs (a and b), the length of the hypotenuse (c) can be found using the formula ( c = \sqrt{a^2 + b^2} ). Conversely, if you have one leg and the hypotenuse, you can rearrange the formula to find the missing leg: ( a = \sqrt{c^2 - b^2} ) or ( b = \sqrt{c^2 - a^2} ).
How do you find the perimeter of a triangle given two sides?
You cannot. If the lengths of the two sides are a and b where a>=b, then all that can be said about the third side, c, is that (a - b) < c < (a + b)
Can 7 8 and 9 be side lengths of a right triangle?
Yes... but not of the same right triangle. A right triangle's side lengths a, b, and c must satisfy the equation a2 + b2 = c2.
What is a statement of the triangle inequality theorem?
The triangle inequality theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side. Specifically, if a triangle has sides of lengths (a), (b), and (c), then the following inequalities must hold: (a + b > c), (a + c > b), and (b + c > a). This theorem is fundamental in geometry as it ensures that a valid triangle can be formed with the given side lengths.
What is the rule that we know about side lengths of triangles?
The rule governing the side lengths of triangles is known as the Triangle Inequality Theorem. It states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side. This means that if you have sides of lengths (a), (b), and (c), the following inequalities must hold: (a + b > c), (a + c > b), and (b + c > a). If any of these conditions are not met, a triangle cannot be formed.
How do find the perimeter of a triangle?
The easiest way is if you already have the lengths of all three sides of the triangle. In which case, you simply add their lengths together to acquire the perimeter. However, if you only have the lengths of two sides of a triangle, and it's a right triangle"; you can use the Pythagorean Theorem to determine the length of the third side. Note: Here are some quick definitions of terms that will be used in the following equations. A² will represent the height of the triangle. B² will represent the width of the triangle. C² will represent the hypotenuse of the triangle. The "Hypotenuse" is the longest side of a triangle. A "Right Triangle" is a triangle that has an angle measuring 90°. When using the Pythagorean Theorem; if you're attempting to find hypotenuse of a triangle; you use the formula "A² + B² = C²". That is; you square the two known sides; then add the products. Upon doing that, find the square root of the sum of both numbers, and you have the length of the hypotenuse. Upon finding the missing side's length; add the lengths of all three sides, and the resulting number will be the perimeter of the triangle. If you have the length of one side, and the hypotenuse of a right triangle; and are seeking to find the third side's length; you use the formula "C² - A² = B²" or "C² - B² = A²"; depending on which side your attempting to find the length of. Like in the previous equation, add the lengths of all three sides together to acquire the perimeter.
Measurements of the sides of a right triangle?
In a right triangle, the side lengths follow Pythagora's Theorem: a^2 + b^2 = c^2; where a and b represent the lengths of the legs and c represents the hypotenuse.
If a triangle has side lengths a b and c and if a2 b2 c2 then the converse of the Pythagorean theorem says that the triangle is an?
Right triangle (apex)
