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What is the approximate size of the smallest angle of a triangle whose sides are 4 5 and 8?
Wiki User
∙ 13y ago
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!!)
Wiki User
∙ 13y ago
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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
If the smallest angle of a triangle is 20 degrees and it is included between sides of 4 and 7 then what is the smallest side of the triangle to the nearest tenth?
It is 3.5 units.
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.
What is the smallest angle of a right angle triangle when its hypotenuse is 7.4cm with one of its sides 4.6cm in length?
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.
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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.
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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.
