Answer :
Using the Law of Cosines, the length of side g in triangle EFG is approximately 87 cm.
To find the length of side g in triangle EFG, we can use the Law of Cosines. This law relates the lengths of the sides of a triangle to the cosine of one of its angles. In this case, we're interested in finding the length of side g, opposite the given angle G.
The Law of Cosines states:
c² = a² + b² - 2ab * cos(C)
Where:
- c is the side we want to find (g in this case)
- a and b are the lengths of the other two sides (e and f respectively)
- C is the angle opposite side c (angle G in this case)
Given the values:
- e = 96 cm
- f = 71 cm
- ∠G = 52°
We can substitute these values into the Law of Cosines and solve for g:
g² = 96² + 71² - 2(96)(71) * cos(52°)
Now, we calculate the value of cos(52°):
cos(52°) ≈ 0.6157
Substituting this value into the equation:
g² = 96² + 71² - 2(96)(71) * 0.6157
g² ≈ 9216 + 5041 - 10920 * 0.6157
g² ≈ 9216 + 5041 - 6728.704
g² ≈ 7528.296
Now, we take the square root of both sides to find g:
g ≈ √7528.296
g ≈ 86.81 cm
Rounded to the nearest centimeter, the length of side g is approximately 87 cm.
