0
What is the approximate size of the smallest angle of a triangle whose sides are 4 5 and 8?
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
------------------------------
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
---------------------------------
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!!)
What else can I help you with?
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 triangle with sides of 6.4 cm 8.2 cm and 5.7 cm?
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.
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.
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 triangle with sides of 6.4 cm 8.2 cm and 5.7 cm?
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.
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.
What is the smallest angle of a triangle with a ratio of 2 to 3 to 4?
It depends on whether the ratio refers to the angles of the triangle or the length of the sides.
What is the smallest angle of a triangle with sides of 22 cm by 62 cm by 48 cm?
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.
How many sides a polygon have with an angle 30?
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.
In any triangle the shortest side is across from which angle largest angle middle angle an angle smallest angle?
In any triangle, the shortest side is across from the smallest angle. This relationship holds true due to the triangle inequality theorem, which states that the length of a side is directly related to the measure of its opposite angle. Therefore, as the angles increase in size, the lengths of the sides opposite them also increase.
What you call a triangle where one angle id 90 and none of the sides are the same?
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 2 equal sides but no right angle?
a triangle with two sides the same length and no right angle
Hat is a triangle with no equal sides?
A triangle with no equal sides and no right angle is a scalene triangle
