In ƒ¢ABC, if the lengths of sides a and c are 8 centimeters and 16 centimeters, respectively, and the measure of �ÚC is 35�‹, what is the measure of �ÚA to two decimal places?

To find the measure of angle A in triangle ABC, we can use the Law of Sines. The Law of Sines states that for any triangle, the ratio of the length of a side to the sine of its opposite angle is constant.

Let's denote the measure of angle A as A, the length of side a as a, the measure of angle C as C, and the length of side c as c.

In this problem, we are given the lengths of sides a and c, as well as the measure of angle C. We need to find the measure of angle A.

The Law of Sines formula is:
a/sin(A) = c/sin(C)

Plugging in the given values:
8/sin(A) = 16/sin(35°)

To solve for sin(A), let's cross-multiply:
8 * sin(35°) = 16 * sin(A)

Now, divide both sides by 16:
sin(A) = (8 * sin(35°)) / 16

To find the measure of angle A, we need to take the inverse sine (sin^-1) of both sides:
A = sin^-1((8 * sin(35°)) / 16)

Using a scientific calculator or an online calculator, we can find the value of (8 * sin(35°)) / 16 and then take the inverse sine of that value to find angle A. The result will be the measure of angle A, rounded to two decimal places.

Please note that "ĢABC" mentioned in the question is likely a typographical error.