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What is the relationship between two shorter sides on a triangle and one longer side?
If given that:
- a, b, and c are sides for any triangle,
- A, B, and C are the angles opposite of their sides,
- assuming c is the longest side, then
c2 = a2 + b2 -2ab*cos(C) (Law of Cosines)
c/sin(C) = a/sin(A) = b/sin(B) (Law of Sines)
In a right triangle,
a2 + b2 = c2(Pythagorean Theorem)
What else can I help you with?
What is the relationship between the longest side of a triangle and the measure of the opposite it.?
In a triangle, the longest side is opposite the largest angle. According to the triangle inequality theorem, if one side is longer than another, the angle opposite the longer side must also be larger. Conversely, the smallest side is opposite the smallest angle. This relationship helps in determining the relative lengths of sides and measures of angles within a triangle.
What is the ratio between the lengths of the two legs of ab30-60-90 triangle?
The length of the longer leg equals the length of the shorter leg times the square root of three.
Does 3.1 4.3 and10.9 make a triangle?
No.To make a triangle the sum of the two shorter sides mustbe longer than the third. With 3.1, 4.3, 10.9 the two shorter sides are 3.1 and 4.3 which have a length sum of 3.1 + 4.3 = 7.4 which is not longer than 10.9, so 3.1, 4.3 and 10.9 cannot form a triangle.
What could be a ratio between lengths of two legs of a 30-60-90 triangle?
In a 30-60-90 triangle, the ratio of the lengths of the two legs is 1:√3. Specifically, the leg opposite the 30-degree angle (shorter leg) is half the length of the hypotenuse, while the leg opposite the 60-degree angle (longer leg) is √3 times the length of the shorter leg. Thus, if the shorter leg is ( x ), the longer leg will be ( x\sqrt{3} ).
Could the segments 6 5 and 12 form a triangle?
No. To form a triangle the sum of the shorter two sides MUST be greater than the longer side. 6 + 5 = 11 < 12 → cannot be a triangle.
What triangle has two equal sides and one longer one?
An isosceles triangle. It is an isosceles triangle even if the third side is shorter.
What is true about the lengths of the three sides of a triangle?
For a triangle to exist, the sum of the shorter two sides must be longer than the third side.
Are true statements about a 30-60-90 triangle?
.The hypotenuse is twice as long as the shorter leg The longer leg is twice as long as the shorter leg.
How do you find the hypotenuse and longer leg of a 30 60 90 triangle?
If you have the shorter legs length, then for the hypotenuse, just multiply the shorter leg by 2. For the longer leg, multiply the shorter leg by the square root of 3.
What is the relationship between the longest side of a triangle and the measure of the opposite it.?
In a triangle, the longest side is opposite the largest angle. According to the triangle inequality theorem, if one side is longer than another, the angle opposite the longer side must also be larger. Conversely, the smallest side is opposite the smallest angle. This relationship helps in determining the relative lengths of sides and measures of angles within a triangle.
The hypotenuse of a triangle is 15 feet long The longer of the two legs is three feet longer than the other Find the length of the shorter leg?
The shorter leg is 9 feet long
The hypotenuse of a triangle is 10 feet long The longer of the two legs is two feet longer than the other Find the length of the shorter leg?
The shorter leg is 6 feet long
He length of the longer leg of a right triangle is 3ft more than three times the length of the shorter leg. The length of the hypotenuse is 4ft more than three times the length of the shorter leg. Fin?
The length of the longer leg of a right triangle is 3ftmore than three times the length of the shorter leg. The length of the hypotenuse is 4ftmore than three times the length of the shorter leg. Find the side lengths of the triangle.
How long is the longer side of a golden triangle when the shorter side is 7 inches?
A golden triangle is an isosceles triangle such that bisecting one of the equal angles produces a new triangle that is similar to the original. It can be shown that the original triangle must be 72-72-36 degrees. Using trigonometry, or the similarity, it can be shown that the long sides were (1+Φ) times the shorter, where Φ is the golden ratio. So with the shorter side being 7 inches, the longer were 18.3 inches, approx.
What is the ratio between the lengths of the two legs of ab30-60-90 triangle?
The length of the longer leg equals the length of the shorter leg times the square root of three.
What is the relationship between wavelength and hue, and how does it compare to the relationship between brightness and which other attribute?
The relationship between wavelength and hue is that shorter wavelengths correspond to cooler colors like blue and longer wavelengths correspond to warmer colors like red. This relationship is similar to the relationship between brightness and intensity, where higher brightness levels correspond to higher intensity levels.
Does 3.1 4.3 and10.9 make a triangle?
No.To make a triangle the sum of the two shorter sides mustbe longer than the third. With 3.1, 4.3, 10.9 the two shorter sides are 3.1 and 4.3 which have a length sum of 3.1 + 4.3 = 7.4 which is not longer than 10.9, so 3.1, 4.3 and 10.9 cannot form a triangle.
