What is the cosine of the angle opposite the side of length 5.64 meters in a triangle with sides 3.18 meters, 7.82 meters, and 5.64 meters?

To find the cosine of the angle opposite to the side of length 5.64 meters, we can use the Law of Cosines. The Law of Cosines states that for any triangle with sides of lengths a, b, and c, and the angle opposite side c, the formula is:

c² = a² + b² – 2ab * cos(C)

In our case, we can denote:

• a = 3.18 meters
• b = 7.82 meters
• c = 5.64 meters

Now, we can plug these values into the Law of Cosines formula:

5.64² = 3.18² + 7.82² – 2 * 3.18 * 7.82 * cos(C)

This simplifies to:

31.8096 = 10.1124 + 61.0724 – 49.7408 * cos(C)

Now, let’s combine the right side:

31.8096 = 71.1848 – 49.7408 * cos(C)

Next, we will isolate the cosine term:

49.7408 * cos(C) = 71.1848 – 31.8096

49.7408 * cos(C) = 39.3752

Now we divide both sides by 49.7408:

cos(C) = 39.3752 / 49.7408

cos(C) ≈ 0.7934

Therefore, the cosine of the angle opposite the side of length 5.64 meters is approximately 0.7934.