I found an answer from www.quora.com

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** ...

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**, D**12d**, C34i, --, U77i, K02i, **24**, **48**, 26, **24**{
3} +2{**12**}.

For more information, see List of uniform polyhedra - Wikipedia

I found an answer from www.khanacademy.com

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

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

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**.

For more information, see Solving General **Triangles**

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}