Question

Find degree of angle with 2 sides of 14 and 5

Answer 1

To find the degree of an angle given two sides of a triangle, you can use the law of cosines. The formula is:

`\[ c^2 = a^2 + b^2 - 2ab \cdot \cos(C) \]`

Where
`\(a\)` and
`\(b\)` are the lengths of the sides of the triangle and
`\(C\)` is the angle opposite side \(c\).

Let's denote the sides as follows:

`\(a = 14\)` (one side)

`\(b = 5\)` (another side)

`\(c\)` would be the side opposite to the angle we're trying to find.

To find the angle
`\(C\)`, we rearrange the law of cosines formula:

`\[ \cos(C) = (a^2 + b^2 - c^2)/(2ab) \]`

In this case, we're looking to find angle
`\(C\)` opposite to the side of length 14 and 5. Substituting the given values:

`\[ \cos(C) = (14^2 + 5^2 - c^2)/(2 * 14 * 5) \]`

`\[ \cos(C) = (196 + 25 - c^2)/(140) \]`

\
`[ \cos(C) = (221 - c^2)/(140) \]`

Now, let's solve for
`\(c^2\):`

`\[ 221 - c^2 = 140 \cdot \cos(C) \]`

`\[ c^2 = 221 - 140 \cdot \cos(C) \]`

`\[ c^2 = 221 - 140 \cdot \cos(C) \]`

To find the degree of angle
`\(C\),` take the inverse cosine (arccos) of the value obtained for
`\(\cos(C)\):`

`\[ C = \arccos\left((221 - c^2)/(140)\right) \]`

Please note that to compute the exact degree of angle
`\(C\),` we need to know the exact length of the third side
`\(c\)` or have further information about the triangle. If you have the value of the side
`\(c\),` you can substitute it into the equation to find the degree of angle
`\(C\).`

Answer 2

5.6 is the right answer.