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Why approximate? I will show you what you should know being in the trig section. Law of cosines. Degree mode!!

a = 4 (angle opposite = alpha)

b = 5 ( angle opposite = beta)

c = 8 ( angle opposite = gamma )

a^2 = b^2 + c^2 - 2bc cos(alpha)

4^2 = 5^2 + 8^2 - 2(5)(8) cos(alpha)

16 = 89 - 80 cos(alpha)

-73 = -80 cos(alpha)

0.9125 = cos(alpha)

arcos(0.9125) = alpha

alpha = 24.15 degrees

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b^2 = a^2 + c^2 - 2bc cos(beta)

5^2 = 4^2 + 8^2 - 2(4)(8) cos(beta)

25 = 80 - 64 cos(beta)

-55 = -64 cos(beta)

0.859375 = cos(beta)

arcos(0.859375) = beta

beta = 30.75 degrees

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Now to find gamma, subtract from 180 degrees

180 - 24.15 - 30.75

= 125.1 degrees

alpha = 24.15 degrees ( subject to rounding, but all add to 180 degrees )

beta = 30.75 degrees

gamma = 125.1 degrees

now you see the smallest, the angle opposite the a side, which is 4

( be in degree mode!!)

Q: What is the approximate size of the smallest angle of a triangle whose sides are 4 5 and 8?

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Not always because the largest angle of a right angle triangle is between its smallest sides which measures 90 degrees

It is 3.5 units.

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.

The smallest angle will be opposite the smallest side of the triangle and so by using the cosine rule it works out as 43.84 degrees.

The smallest angle of the triangle is opposite to its smallest side which is 4.6cm and so by using the sine rule: A/a = B/b = C/b the smallest angle works out as 38.43 degrees rounded to two decimal places.

Related questions

Not always because the largest angle of a right angle triangle is between its smallest sides which measures 90 degrees

It is 3.5 units.

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.

The smallest angle will be opposite the smallest side of the triangle and so by using the cosine rule it works out as 43.84 degrees.

The smallest angle of the triangle is opposite to its smallest side which is 4.6cm and so by using the sine rule: A/a = B/b = C/b the smallest angle works out as 38.43 degrees rounded to two decimal places.

It depends on whether the ratio refers to the angles of the triangle or the length of the sides.

The smallest angle of the triangle will be opposite the smallest side and using the cosine rule it works out as 17.9 degrees rounded to one decimal place.

Smallest possible interior angle of regular polygon is 60 degrees (triangle). The greater the number of sides, the greater each interior angle. If exterior angle is 30 degrees, the polygon has 12 sides.

It is simply a right angle triangle but if the sides were the same then it is an isoceles right angle triangle

a triangle with two sides the same length and no right angle

A triangle with no equal sides and no right angle is a scalene triangle

The given dimensions will not form any kind of triangle because the sum of its 2 smallest sides is equal to its longest side and so therefore finding the largest angle is not possible.