Final answer:
The length of side g in Δefg can be found using the Law of Cosines with the given measurements of sides e, f, and the angle ∠g. You substitute the values into the formula to calculate g² and then take the square root to find the length of side g, rounding to the nearest centimeter.
Step-by-step explanation:
To find the length of side g in triangle Δefg, we can apply the Law of Cosines, as we have the lengths of sides e and f and the measurement of angle ∠g. The Law of Cosines is stated as:
c² = a² + b² - 2ab·cos(γ)
Where c is the length of the side opposite angle γ, and a and b are the lengths of the other two sides of the triangle.
In this case, to find the length of side g, we use:
g² = e² + f² - 2ef·cos(∠G)
Substituting the given values:
g² = 300² + 910² - 2·(300)·(910)·cos(152°)
Calculating the value of g, we make sure to round to the nearest centimeter as requested.