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What are the smallest and largest angles of a triangle with sides 7.6cm 9.2cm and 5.7cm?
The largest angle is opposite the largest side.
Using the cosine rule:
9.2² = 7.6² + 5.7² - 2 × 7.6 × 5.7 × cos β
→ cos β = (7.6² + 5.7² - 9.2²) / (2 × 7.6 × 5.7)
→ β = arccos((7.6² + 5.7² - 9.2²) / (2 × 7.6 × 5.7)) ≈ 86.29°
The smallest angle is opposite the shortest side.
The cosine rule can be used again, or using the sine rule:
sin γ / 5.7 = sin 86.29° / 9.2
→ sin γ = sin 86.29° × 5.7 / 9.2
→ γ = arcsin(sin 86.29° × 5.7 / 9.2) ≈ 38.19°
What else can I help you with?
What are the angles from smallest to greatest in a triangle that has sides of 8.3cm 5.4cm and 7.1cm?
If you know all three sides of a triangle, you can calculate the angles using the law of cosines. If you only want to know which angle is the smallest, it is much simpler: The angle that is opposite to the smallest side is the smallest angle; the angle that is opposite to the largest side is the largest angle.
Is the largest side of a triangle is opposite from the largest angle?
Yes, in a triangle, the largest side is always opposite the largest angle. This is a fundamental property of triangles, known as the triangle inequality theorem. Conversely, the smallest side is opposite the smallest angle. This relationship helps in determining the relative sizes of the sides and angles within any triangle.
What is the sorting rule for I triangle?
The sorting rule for a triangle typically refers to the arrangement of its sides or angles based on specific criteria. For sides, triangles can be sorted by length, with the longest side being the largest and the shortest side being the smallest. For angles, triangles are often sorted by their measure, from the smallest angle to the largest. Additionally, triangles can be classified into types such as acute, right, or obtuse based on their angle measures.
What is the smallest angle of a triangle with a ratio of 2 to 3 to 4?
It depends on whether the ratio refers to the angles of the triangle or the length of the sides.
Is it true that the largest angle of a triangle is between the two longest sides?
Not always because the largest angle of a right angle triangle is between its smallest sides which measures 90 degrees
What are the angles from smallest to greatest in a triangle that has sides of 8.3cm 5.4cm and 7.1cm?
If you know all three sides of a triangle, you can calculate the angles using the law of cosines. If you only want to know which angle is the smallest, it is much simpler: The angle that is opposite to the smallest side is the smallest angle; the angle that is opposite to the largest side is the largest angle.
Is the largest side of a triangle is opposite from the largest angle?
Yes, in a triangle, the largest side is always opposite the largest angle. This is a fundamental property of triangles, known as the triangle inequality theorem. Conversely, the smallest side is opposite the smallest angle. This relationship helps in determining the relative sizes of the sides and angles within any triangle.
What shape has the smallest number of sides a regular polygon with obtuse angles can have?
An obtuse triangle has 3 sides.
What is the sorting rule for I triangle?
The sorting rule for a triangle typically refers to the arrangement of its sides or angles based on specific criteria. For sides, triangles can be sorted by length, with the longest side being the largest and the shortest side being the smallest. For angles, triangles are often sorted by their measure, from the smallest angle to the largest. Additionally, triangles can be classified into types such as acute, right, or obtuse based on their angle measures.
What is the relation between the angles and sides of a triangle?
In one triangle, the largest side corresponds to the largest angle and vice versa.
What is the classification of the triangle?
A triangle can be classified according to its sides or the magnitude of its largest angle (two of the angles MUST be acute angles). All three sides equal: equilateral. Such a triangle must be equiangular, but that term is rarely used. Two equal angles, third one different (or two sides equal and third different): isosceles. All three angles different (all three sides different): scalene. Largest angle = 90 degrees: A right angled triangle. Largest angle obtuse: An obtuse angled triangle.
What is the smallest angle of a triangle with a ratio of 2 to 3 to 4?
It depends on whether the ratio refers to the angles of the triangle or the length of the sides.
Is it true that the largest angle of a triangle is between the two longest sides?
Not always because the largest angle of a right angle triangle is between its smallest sides which measures 90 degrees
Triangle with no equal sides angles or sides?
A triangle with no equal sides or angles will always be classified as 'scalene'.
How many sides and angles does a scalene triangle have?
Sides and Angles in a TriangleBy definition, a triangle has three sides. Since the number of sides and angles is equal, it would also have three angles.
All angles are right angles or a triangle has four sides?
False - and false ! Not ALL angles are right-angles - and a triangle has THREE sides !
What is the relationship between the lengths of the sides and the measures of the angles in a triangle?
Relationship between the lengths and the measures of angles are related to theorems like the opposite side of the largest angle is the largest side two equal angles oppositee sides are also equal
