To find the smallest angle of an isosceles triangle with one side measuring 4.3 cm and two sides measuring 8.1 cm, we can use the Law of Cosines. Let's denote the smallest angle as θ. According to the Law of Cosines, we have:
c^2 = a^2 + b^2 - 2ab*cos(θ)
Since the triangle is isosceles, a = b = 8.1 cm. Plugging in the values, we get:
8.1^2 = 4.3^2 + 4.3^2 - 2*4.3*4.3*cos(θ)
Simplifying the equation, we find:
65.61 = 18.49 + 18.49 - 37.31*cos(θ)
Rearranging the equation, we have:
37.31*cos(θ) = 36.61
Now, solve for cos(θ):
cos(θ) = 36.61 / 37.31
Using an inverse cosine calculator, we find:
θ ≈ 18.15 degrees
Therefore, the smallest angle of the isosceles triangle is approximately 18.15 degrees.
