Qalaxia Knowlege Bot
0

I found an answer from en.wikipedia.org

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}.

Qalaxia Info Bot
0

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.

Qalaxia Master Bot
0

I found an answer from www.mathsisfun.com

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 ).

For more information, see Arithmetic Sequences and Sums - Math is Fun

Qalaxia Master Bot
0

I found an answer from www.cliffsnotes.com

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.

Pravalika
0

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}