Find the angle α. One side is 25, the other side is 20 and the other side is 18. The angle α is between sides with length 25 and 18.

Answer 1

For this triangle problem, you will use the Law of Cosines to solve for angle α. There are three "versions" of the Law of Cosines. Be sure to choose the one containing α, A, B, and C.

The variable in the equations are:

α = the angle across from side A

b = the angle across from side B

c = the angle across from side C

A = side A

B = side B

C = side C

The Law of Cosines:

A^2 = B^2 + C^2 - 2BC * cos(α)

Since angle α is between the sides measuring 18 and 25, we can deduce that side A is 20, because side A is across from angle α. The other two sides are 18 and 25. It doesn't matter which one is B and which one is C, but usually C will have the longest measure. Note though, that this triangle is NOT a right triangle. The law of cosines is used to solve triangles that are not right triangles.

A = 20

B = 18

C = 25

α = ?

Plug your values into the equation:

A^2 = B^2 + C^2 - 2BC * cos(α)

20^2 = 18^2 +25^2 - 2(18)(25)*cos(α)

Simplify:

400 = 324 + 625 - 900 * cos(α)

400 = 949 - 900 * cos(α)

Isolate the term with cosine:

-0.61 = cos(α)

Take the inverse cosine to solve for α

α = cos^-1(-0.61)

α = 127.5895 degrees

If you were asked to also find the other two angles, b and c, you could use the Law of Sines from here.

Hope this helped!

Answer 2