law of cosines - The smallest angle of the triangle whose sides are 6 + \sqrt{12}, \sqrt{48}, \sqrt{24}

The smallest angle of the triangle whose sides are 6 + \sqrt{12}, \sqrt{48}, \sqrt{24}

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law of cosines the smaller angle of the triangle whose sides are given

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Qalaxia QA Bot (last edited 2 years ago)

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What is the smallest angle of a triangle whose sides are 6+root 12 ...

What is the smallest angle of a triangle whose sides are 6+root 12, root 48 and root 24?

For more information, see What is the smallest angle of a triangle whose sides are 6+root 12 ...

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List of uniform polyhedra - Wikipedia

In geometry, a uniform polyhedron is a polyhedron which has regular polygons as faces and is ... [W] Wenninger, 1974, has 119 figures: 1-5 for the Platonic solids, 6-18 for the ... dodecahedron and icosahedron with 4, 6, 8, 12, and 20 sides respectively. ... 3.3.3.12, | 2 2 12, D12d, C34i, --, U77i, K02i, 24, 48, 26, 24{ 3} +2{12}.

For more information, see List of uniform polyhedra - Wikipedia

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Trig challenge problem: maximum value (video) | Khan Academy

Sal solves a very complicated algebraic trig problem that appeared as problem 48 in the 2010 IIT JEE Paper I exam.

For more information, see Trig challenge problem: maximum value (video) | Khan Academy

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Arithmetic Sequences and Sums - Math is Fun

Arithmetic Sequences and Sums. Sequence. A Sequence is a set of things ... a term (or sometimes "element" or "member"), read Sequences and Series for more details. Arithmetic Sequence. In an Arithmetic Sequence the difference between one term and the next is a ... (We use "n−1" because d is not used in the 1st term ).

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Solving General Triangles

The following is a listing of these categories along with a procedure to follo. ... SSS: If the three sides of a triangle are known, first use the Law of Cosines to find one ... Next, use the Law of Sines to find the smaller of the two remaining angles.

For more information, see Solving General Triangles

Pravalika (last edited 2 years ago) (Student, UG2 Grade)

Required formula:

The law of cosines is a rule that relates the cosine of a given angle to the three sides of a triangle.

Law of Cosines. \cos \theta = \frac{a^2 + b^2 - c^2}{2ab}

Step 1: Using the cosine law, find the smallest angle of the triangles

Given sides of the triangle

a = 6 + \sqrt{12}, b = \sqrt{48}, \text{ and } c = \sqrt{24}

We know that: The shortest side is on the opposite side of the smallest angle.

Thus, C is the smallest angle of the triangle since c is the smallest side

\cos C = \frac{(6 + \sqrt{12})^2 + (\sqrt{48}) - ( \sqrt{24})^2}{2( 6 + \sqrt{12})(\sqrt{48})}

\cos C = \frac{(6^2 + (\sqrt{12})^2 + 12\sqrt{12}) + 48 - 24}{2( 6 + \sqrt{12})(\sqrt{48})}

\cos C=\frac{36+12+12\sqrt{12}+48-24}{2(6+\sqrt{12})(\sqrt{48})}

\cos C = \frac{72 + 12\sqrt{12}}{2( 6 + \sqrt{12})(\sqrt{48})}

\cos C = \frac{12(6 + \sqrt{12})}{2( 6 + \sqrt{12})(\sqrt{48})}

\cos C = \frac{6}{\sqrt{48}}

\cos C = \frac{6}{4\sqrt{3}} = \frac{3}{2\sqrt{3}}

\cos C = \frac{\sqrt{3}}{2}

\cos C = \cos \frac{\pi}{6}

C = \frac{\pi}{6}

Hence, the smallest angle of the triangle C = \frac{\pi}{6}