In ΔTUV, t = 670 cm, u = 510 cm and ∠V=159°. Find the length of v, to the nearest centimeter.

To find the length of side v in triangle TUV, 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 an angle γ opposite side c, the following relationship holds:

c² = a² + b² - 2ab*cos(γ)

In this case, we know that side t = 670 cm, side u = 510 cm, and ∠V = 159°. We want to find the length of side v, which is opposite ∠V. Therefore, we can plug these values into the Law of Cosines:

v² = t² + u² - 2tucos(V) v² = (670 cm)² + (510 cm)² - 2(670 cm)*(510 cm)*cos(159°)

Now, we just need to calculate the right-hand side. Remember to convert the angle to radians before using the cosine function, as most calculators and programming languages use radians, not degrees.

After calculating, we take the square root of the result to find the length of side v.

Please note that the result should be rounded to the nearest centimeter as per the problem statement.