What Is The Largest Possible Angle In A Triangle?

You guess smallest possible angle is 1 and largest possible angle is 178 for triangle.

Triangle with this angles have angles 1, 1, 178 as you know the sum of all angles of a triangle is 180.

We can take an angle which is less than 1.

What is the largest angle in a triangle?

In a triangle: The shortest side is always opposite the smallest interior angle. The longest side is always opposite the largest interior angle.

Which regular polygon has the largest internal angle?

The polygon with the least number of sides is a triangle. A regular triangle will be an equilateral triangle and each of its angles will be 60 degrees and that is the least interior angle. There is no limit to the largest interior angle of a regular polygon.

How do you find the angle of a triangle?

Answer: If you know two angles, then you can work out the third since all the angles sum to 180 degrees. If the sides are a, b and the hypotenuse is c (opposite angle A), and the angles are A, B and C, then Sin A = a/c, so a = cSin A. Also Cos A = b/c, so b = cCos A.

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Which is the smallest angle?

Always remember that the smallest angle in a triangle is always opposite the shortest side. Also, the biggest angle is always opposite the longest side. answer: The smallest angle is 55.49 degrees rounded to two decimal places.

What is the longest side of a triangle?

The hypotenuse is always opposite the right angle and it is always the longest side of the triangle.

How do you find the missing angle in a triangle?

Step 2: Add together the two known angles inside the triangle. To determine to measure of the unknown angle, be sure to use the total sum of 180°. If two angles are given, add them together and then subtract from 180°. If two angles are the same and unknown, subtract the known angle from 180° and then divide by 2.

Can 22 degree be an interior angle of a regular polygon?

If 22° is an interior angle, then 180° – 22°, i.e. 158° is exterior angle. Thus, 22° cannot be an interior angle of a regular polygon.

What is a 50 sided polygon called?

In geometry, a pentacontagon or pentecontagon or 50-gon is a fifty-sided polygon.

Is there a minimum number of acute interior angles?

Any convex polygon can have at most 3 acute interior angles. For any acute interior angle, the exterior angle will be greater than 90 degrees. The sum of all exterior angles in a polygon is always 360 degrees, so there cannot be 4 or more acute interior angles.

How do you find an angle of a triangle with 3 sides?

Example

  • Step 1 The two sides we know are Adjacent (6,750) and Hypotenuse (8,100).
  • Step 2 SOHCAHTOA tells us we must use Cosine.
  • Step 3 Calculate Adjacent / Hypotenuse = 6,750/8,100 = 0.8333.
  • Step 4 Find the angle from your calculator using cos-1 of 0.8333:

How do you find the angle of a triangle with two angles?

To find the third angle of a triangle when the other two angles are known subtract the number of degrees in the other two angles from 180o.

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How do you find the angle of a right triangle?

Key Points

  1. The Pythagorean Theorem, a2+b2=c2, a 2 + b 2 = c 2 , is used to find the length of any side of a right triangle.
  2. In a right triangle, one of the angles has a value of 90 degrees.
  3. The longest side of a right triangle is called the hypotenuse, and it is the side that is opposite the 90 degree angle.

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 longest side of a triangle called?

hypotenuse

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.

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.

What side of a triangle is A?

The sides of the triangle are known as follows: The hypotenuse is the side opposite the right angle, or defined as the longest side of a right-angled triangle, in this case h. The opposite side is the side opposite to the angle we are interested in, in this case a.

Does the Pythagorean theorem work for every triangle?

Pythagoras’ theorem states that for all right-angled triangles, ‘The square on the hypotenuse is equal to the sum of the squares on the other two sides’. Pythagoras’ theorem only works for right-angled triangles, so you can use it to test whether a triangle has a right angle or not.

How do you find the degree of an angle?

If two of the angles of a triangle have measures of 60 and 80 degrees, add the numbers together to get a sum of 140. Then, subtract this sum from the total angle measure for a triangle, which is 180 degrees: 180 – 140 = 40 degrees.

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How do you solve the SSA triangle?

Solving SSA Triangles

  • use The Law of Sines first to calculate one of the other two angles;
  • then use the three angles add to 180° to find the other angle;
  • finally use The Law of Sines again to find the unknown side.

How do you solve a SAS triangle?

Solving SAS Triangles

  1. use The Law of Cosines to calculate the unknown side,
  2. then use The Law of Sines to find the smaller of the other two angles,
  3. and then use the three angles add to 180° to find the last angle.

Can a triangle have only one acute angle?

Never one acute angle!! Because one acute means two obtuse angles each greater the 90 degrees. The two obtuse angles then add up to greater than 180 degrees. But the three angles of a triangle must add to exactly 180 deg, So there must be at least two acute angles.

Can a triangle have no acute angles?

Since a triangle’s angles must sum to 180° in Euclidean geometry, no Euclidean triangle can have more than one obtuse angle. Acute and obtuse triangles are the two different types of oblique triangles — triangles that are not right triangles because they have no 90° angle.

What is the smallest number of acute angles in a triangle?

Given that the inside angles of a standard 2 dimensional triangle equal 180 degrees, and the smallest non-acute angle is 90 degrees, at least two of those 3 inside angles must be < 90 degrees, thus acute.
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