Question

If in triangle ABC, a=5, b=6 and c=8, then cos A is...

Answer 1

Using the Law of Cosines, cos A for triangle ABC with sides a=5, b=6, and c=8 is calculated to be -1/20.

Step-by-step explanation:

To find the value of cos A for triangle ABC with the sides a=5, b=6, and c=8, we can use the Law of Cosines. According to this law, to solve for an angle in a non-right triangle when we know the lengths of all three sides, we can use the formula:

c² = a² + b² - 2ab cos(y)

Here, we need to find cos(A), so we will re-arrange the formula to solve for cos(A):

cos(A) = (a² + b² - c²) / (2ab)

Plugging in the known values, we get:

cos(A) = (5² + 6² - 8²) / (2 * 5 * 6)

cos(A) = (25 + 36 - 64) / (60)

cos(A) = (-3) / (60)

cos(A) = -1/20

Therefore, cos A in triangle ABC is -1/20.

Answer 2

In a triangle, the nomenclature is that a variable side a is opposite of the angle A. we can use the cosine law to determine the value of cosine A.
a2 = b2 + c2 -2bc cos a25 = 36 + 64 - 2*6*8 * cos acos a = 25/32