Quick Answer: Can 30 60 90 Angles Make A Triangle?

Are all 30-60-90 triangles similar?

Triangles with the same degree measures are similar and their sides will be in the same ratio to each other.

This means that all 30-60-90 triangles are similar, and we can use this information to solve problems using the similarity..

What type of triangle is 60 60 60?

This is a 60-60-60 triangle (that is, an equilateral triangle), with sides having a length of two units.

What are the lengths of a 30 60 90 Triangle?

What is a 30-60-90 Triangle? 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.

Which side is the short leg of this 30 60 90 Triangle?

Hypotenuse​Relationship Between the. ​Short Leg and Hypotenuse The short leg of a 30-60-90 triangle is always 1/2 the length of the hypotenuse.

What are the rules for a 45 45 90 Triangle?

45°-45°-90° Triangles In a 45°−45°−90° triangle, the length of the hypotenuse is √2 times the length of a leg. To see why this is so, note that by the Converse of the Pythagorean Theorem , these values make the triangle a right triangle. Note that an isosceles right triangle must be a 45°−45°−90° triangle.

What is the maximum number of right angles that can be in a triangle?

Explanation: A triangle has 180o as the sum of all its internal angles, no more, no less. If one angle is 90o , then you can have two 45o angles, one 30o and a 60o , an 81o and a 9o – pretty much any combination of numbers adding up to 90 to make the total 90+90=180 .

How many 90 degree angles are in a triangle?

The right triangle has one 90 degree angle and two acute (< 90 degree) angles. Since the sum of the angles of a triangle is always 180 degrees...

How do you find the sides of a 30 60 90 Triangle?

30-60-90 Triangle RatioShort side (opposite the 30 degree angle) = x.Hypotenuse (opposite the 90 degree angle) = 2x.Long side (opposite the 60 degree angle) = x√3.Apr 14, 2020

How do you do special right triangles?

Step 1: This is a right triangle with two equal sides so it must be a 45°-45°-90° triangle. Step 2: You are given that the both the sides are 3. If the first and second value of the ratio x:x:x√2 is 3 then the length of the third side is 3√2. Answer: The length of the hypotenuse is 3√2 inches.

Can a triangle have a 1 degree angle?

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.

What type of triangle has all angles measuring 60?

equilateral triangleAn equilateral triangle has all three sides equal, and all three interior angles equal, too. In this case, each interior angle of an equilateral triangle is 60 degrees. An equilateral triangle is sometimes referred to as an equiangular triangle because all three angles are equal.

What is the rule for a 30-60-90 Special right triangle choices are given by the order of short leg long leg hypotenuse leg?

Qualities of a 30-60-90 Triangle The hypotenuse is equal to twice the length of the shorter leg, which is the side across from the 30 degree angle. The longer leg, which is across from the 60 degree angle, is equal to multiplying the shorter leg by the square root of 3.

What are the lengths of a 45 45 90 Triangle?

A 45°-45°-90° triangle is a special right triangle that has two 45-degree angles and one 90-degree angle. The side lengths of this triangle are in the ratio of; Side 1: Side 2: Hypotenuse = n: n: n√2 = 1:1: √2. The 45°-45°-90° right triangle is half of a square.

Do angles of a triangle equal 180?

In a Euclidean space, the sum of angles of a triangle equals the straight angle (180 degrees, π radians, two right angles, or a half-turn). …

How do you find the height of a 60 60 60 Triangle?

Explanation: An equilateral triangle has three congruent sides, and is also an equiangular triangle with three congruent angles that each meansure 60 degrees. To find the height we divide the triangle into two special 30 – 60 – 90 right triangles by drawing a line from one corner to the center of the opposite side.

Can you have a triangle with all the three angles less than 60 degree?

No, a triangle cannot have all angles less than 60°, because if all angles will be less than 60°, then their sum will not be equal to 180°. Hence, it will not be a triangle.

How do you find the longer leg of a 30 60 90 Triangle?

In any 30-60-90 triangle, you see the following: The shortest leg is across from the 30-degree angle, the length of the hypotenuse is always double the length of the shortest leg, you can find the long leg by multiplying the short leg by the square root of 3.

What is the 30 60 90 Triangle rule?

Tips for Remembering the 30-60-90 Rules Remembering the 30-60-90 triangle rules is a matter of remembering the ratio of 1: √3 : 2, and knowing that the shortest side length is always opposite the shortest angle (30°) and the longest side length is always opposite the largest angle (90°).

Which of the following are true statements about a 30 60 90 Triangle?

Answer Expert Verified A 30-60-90 triangle is a right triangle with one leg equal to x, the other leg equal to 2x and the hypotenuse equal to x*sqrt(3). So, there you see that the longer leg is twice as long as the shorter leg (option D) and the hypotenuse is sqrt(3) times as long as the shorter leg (option F).

How do you find the length of the third side of a triangle?

If a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse, then the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.