This is a topic that comes up from time to time for our subject matter specialists. Now, we have the full, extensive explanation as well as the solution for everyone who is interested!

If we know either two sides and the angle that separates them or three sides but no angles, we may apply the law of cosines to determine the length of any angle or side in a triangle that is not a right triangle.

#### Are right triangles the only shapes for which sin and cos may be used?

The following trigonometric ratios, when applied to right triangles, will always be accurate regardless of the size of the triangle they are applied to. It is important to keep in mind that the Sine, Cosine, and Tangent ratios are the fundamental trigonometric ratios. These ratios are named from the Greek term for the measurement of triangles, and they are Sine, Cosine, and Tangent, respectively.

#### Does the SOH CAH TOA method work for triangles that aren’t right angles?

Pythagoras’ Theorem and SOHCAHTOA may be used to solve problems with triangles with right angles. These strategies, on the other hand, are not applicable to triangles with angles that are not right angles.

#### Are you able to solve a triangle that is not right?

However, it would be better to have procedures that we can immediately apply to non-right triangles without first having to construct right triangles. This would eliminate the need for us to create right triangles. Oblique triangles may be defined as any other kind of triangle outside right triangles. Finding the measurements of all three angles and all three sides of an oblique triangle is required in order to solve the triangle.

#### Which side of a triangle with sides measuring 30, 60, and 90 degrees is the shortest?

And this goes on. Because thirty degrees is the lowest angle possible, the side that is perpendicular to that degree will always be the shortest. Because sixty degrees is the medium-sized angle in this triangle, the length of the side that is perpendicular to the sixty-degree angle will be the middle length.

**37 questions found in relevant categories**

#### Is the Pythagorean theorem applicable to triangles that are not right triangles?

Since Pythagoras’ theorem can only be used to solve problems with triangles with right angles, you may use it to determine whether or not a triangle contains a right angle.

#### How do you do trigonometric non right triangles?

There are two rules, the Sine Rule and the Cosine Rule, that must be followed in order to accomplish this. a/Sin A = b/Sin B = c/Sin C is the formula for the sine rule. (both the lowercase and the uppercase are quite significant.

#### Does the concept of trigonometry apply to each and every triangle?

Even while right triangles make up the vast majority of applications for trigonometric functions, there are circumstances in which these functions may be used with other types of triangles as well. Calculating the third side of a triangle using the trigonometric functions and the law of cosines is possible if you are given two sides and an angle that connects the two sides.

#### What does it imply when it says SOH CAH TOA?

A useful mnemonic called “SOHCAHTOA” may be used to recall the definitions of the trigonometric functions sine, cosine, and tangent. These definitions are as follows: sine equals opposite over hypotenuse, cosine equals adjacent over hypotenuse, and tangent equals opposite over adjacent. (1) (2)

#### What is the formula for a triangle that does not have right angles?

In the year 10 unit titled “Further Trigonometry,” we learned about and proved the sine rule, which is a method for determining the sides and angles of triangles that do not have a right angle. asinA=bsinB=csinC.

#### What name is given to the side that is the longest in a right triangle?

In a right triangle, the side that is perpendicular to the right angle is always considered to be the hypotenuse. In a right triangle, this is the side that is the longest. The terms “opposite” and “adjacent” are used to refer to the two remaining sides.

#### Is it possible to apply trig ratios on triangles that are not right triangles?

We have only discussed right triangles up until this point, but trigonometry can be simply applied to other types of triangles as well. This is due to the fact that every other kind of triangle can be split into two right triangles by using an altitude.

#### Why is it that trigonometry can only be used to solve problems with right triangles?

Trigonometry is used to solve any triangle with a right angle because we know that the sum of the angles in a triangle is 180, and if the triangle has a right angle, then the other angles are less than 90. This means that the triangle will fall into the first quadrant, in which the values of sin, cos, and tan will all be positive. However, as we move further into the second quadrant, cos and tan will take on negative values, and in the third quadrant

#### Is the hypotenuse a property that only exists in right triangles?

Yes, the hypotenuse is always the triangle with the longest side, but this is only the case for triangles with right angles. In the case of isosceles triangles, the two equal sides are referred to as the legs, but in the case of equilateral triangles, all three sides are simply referred to as sides.

#### How exactly does one use the Pythagorean theorem in order to determine which triangles are right triangles?

**Key Points**

- It is possible to determine the length of any one of the sides of a right triangle by using the Pythagorean Theorem, which states that a2 + b2 = c2.
- One of the angles of a right triangle has a value of 90 degrees, indicating that the triangle is a right triangle.
- The side that is perpendicular to the angle that makes up a right triangle is known as the hypotenuse, and it is the side that is the longest overall.

#### Can the Pythagorean theorem be applied to any triangle at all?

The Pythagorean Theorem, or more accurately, its opposite, may be used to any triangle in order to determine whether or not the triangle in question is a right triangle.

#### Explain the Pythagorean theorem in layman’s terms, please.

The Pythagorean theorem is a well-known geometric theorem which states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle). This may also be expressed using the standard algebraic notation of a2 + b2 = c2…. Despite this, Pythagoras is generally acknowledged as the creator of the theorem.

#### How do you find a triangle with sides of 30, 60, and 90 degrees?

**Triangle with a Ratio of 30-60-90**

- Equal to x is the short side, which is perpendicular to the angle of 30 degrees.
- The length of the hypotenuse, which is opposite the angle of 90 degrees, equals x.
- = x3 is the length of the side that is perpendicular to the angle of 60 degrees.

#### What is the name given to the side that is the longest in an obtuse triangle?

In an obtuse triangle, the side that is perpendicular to the obtuse angle vertex is the one that is the longest. There are two possible configurations for an obtuse triangle: isosceles (two sides equal in length and two angles equal in length) or scalene (no equal sides or angles).

#### Is it true that the hypotenuse of a non-right triangle is always the longest side of the triangle?

Yes, the hypotenuse is always the triangle with the longest side, but this is only the case for triangles with right angles. In the case of isosceles triangles, the two equal sides are referred to as the legs, but in the case of equilateral triangles, all three sides are simply referred to as sides.

#### Which two things make up the base of a right triangle?

The “legs” of the triangle are a and b, which are the two sides that together form the angle with a measure of 90 degrees. The side of the triangle that is perpendicular to the right angle is referred to as the “hypotenuse,” and it is denoted by the letter c. Another name for an angle that is 90 degrees is a “right angle.” The hypotenuse of a right triangle is also the side that is the longest overall.