Question

определите косинус наибольшего угла треугольника , если стороны равны 7 см,11 см, 14 см

Answer 1

Наибольший угол лежит против наибольшей стороны.

 

Поэтому косинус наибольшего угла (используя теорему косинусов) равен

 

$cos C=\frac{a^2+b^2-c^2}{2ab}; cos C=\frac{7^2+11^2-14^2}{2*7*11}=\frac{-13}{77}$

Answer 2

Finding the Cosine of the Largest Angle in a Triangle

To find the cosine of the largest angle in a triangle with sides of 7 cm, 11 cm, and 14 cm, we can use the law of cosines, which states that for any triangle with sides of lengths a, b, and c and angles opposite those sides A, B, and C, the following equation holds true:

c^2 = a^2 + b^2 - 2ab * cos(C)

In this case, we are interested in finding the cosine of the largest angle, which we can denote as angle C. We can rearrange the law of cosines to solve for cos(C):

cos(C) = (a^2 + b^2 - c^2) / (2ab)

Now, we can substitute the given side lengths into the equation to find the cosine of the largest angle.

Substituting a = 7 cm, b = 11 cm, and c = 14 cm into the equation:

cos(C) = (7^2 + 11^2 - 14^2) / (2 * 7 * 11)

cos(C) = (49 + 121 - 196) / 154

cos(C) = -26 / 154

cos(C) = -0.168

Therefore, the cosine of the largest angle in the triangle with sides of 7 cm, 11 cm, and 14 cm is -0.168. [[7 #]]