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What is the formula for the third side of a triangle?
a2+b2=c2, but that only works for right triangles, where c is opposite the right angle. The law of cosines, see Related Link below, will help for non right triangles, but you need to know one of the angles.
What kind of triangles can the Pythagorean theorem be applied to?
Any right-angled triangle
Why Does pythagorean theorem don't work for non right angle triangles?
The Pythagorean theorem specifically applies to right-angled triangles because it is based on the unique relationship between the lengths of the sides in such triangles. It states that the square of the length of the hypotenuse equals the sum of the squares of the other two sides (a² + b² = c²). In non-right triangles, this relationship does not hold, as the angles and side lengths do not conform to the theorem's criteria. Instead, the Law of Cosines is used for non-right triangles to relate their side lengths and angles.
Will the pythagorean theorem work with the measure of the sides of any triangle?
The Pythagorean theorem only applies to right triangles, where one angle measures 90 degrees. It states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. For triangles that are not right triangles, different formulas, such as the Law of Cosines, must be used to relate the sides and angles.
What problem types can always be solved by using the law of cosines or sines?
The law of cosines and sines can always be used to solve problems involving triangles, specifically when dealing with non-right triangles. The law of cosines is applicable for finding a side or angle when you know either two sides and the included angle or all three sides. The law of sines can be used when you have two angles and one side (AAS or ASA) or two sides and a non-included angle (SSA). Both laws are essential in solving triangle problems in various applications, including navigation and physics.
Can The law of cosines can only be applied to right triangles?
Cosine Rule: a2 = b2+c2-2bc*cos A is applicable to all triangles
Is it true that the law of cosines reduces the Pythagorean theorem with right triangles?
Yes
What is the formula for the third side of a triangle?
a2+b2=c2, but that only works for right triangles, where c is opposite the right angle. The law of cosines, see Related Link below, will help for non right triangles, but you need to know one of the angles.
Can trig functions work on non-right triangles?
Yes. Look up the law of sines and the law of cosines as examples. there are also formulas that can find out the area of a non-right triangle.
How is trigonometry applied?
Trigonometry is applied in construction and building, as trigonometry measures right angled triangles.
What kind of triangles can the Pythagorean theorem be applied to?
Any right-angled triangle
Can trigonometry be applied only in right angled triangles?
No. It can be used on any triangle.
Why Does pythagorean theorem don't work for non right angle triangles?
The Pythagorean theorem specifically applies to right-angled triangles because it is based on the unique relationship between the lengths of the sides in such triangles. It states that the square of the length of the hypotenuse equals the sum of the squares of the other two sides (a² + b² = c²). In non-right triangles, this relationship does not hold, as the angles and side lengths do not conform to the theorem's criteria. Instead, the Law of Cosines is used for non-right triangles to relate their side lengths and angles.
Will the pythagorean theorem work with the measure of the sides of any triangle?
The Pythagorean theorem only applies to right triangles, where one angle measures 90 degrees. It states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. For triangles that are not right triangles, different formulas, such as the Law of Cosines, must be used to relate the sides and angles.
Can trigonometric functions sine cosine and tangent be used in triangles other than right triangles?
Yes, trigonometric functions such as sine, cosine, and tangent can be applied to triangles other than right triangles through the use of the Law of Sines and the Law of Cosines. These laws relate the ratios of the sides of any triangle to the sines and cosines of their angles, allowing for the calculation of unknown sides and angles in non-right triangles. Thus, trigonometric functions are versatile tools applicable to various types of triangles.
What problem types can always be solved by using the law of cosines or sines?
The law of cosines and sines can always be used to solve problems involving triangles, specifically when dealing with non-right triangles. The law of cosines is applicable for finding a side or angle when you know either two sides and the included angle or all three sides. The law of sines can be used when you have two angles and one side (AAS or ASA) or two sides and a non-included angle (SSA). Both laws are essential in solving triangle problems in various applications, including navigation and physics.
Is it true that Pythagorean theorem can only be used for right-angled triangles?
Yes. The Pythagorean Theorem is true for only right triangles. However, a variety of other similar equations can be used for other triangle types. Law of Sines: a/sinA = b/sinB = c/sinC Law of Cosines: c2 = a2 + b2 - 2ab*cosC
