Final answer:
To find side a in triangle ABC, the Law of Cosines is applied using known values of angle A (15 degrees), side b (19), and side c (12). The calculated length of side a is approximately 16.9 to the nearest tenth.
Step-by-step explanation:
We are asked to find side a in triangle ABC, where the measure of angle A is 15 degrees, side b is 19, and side c is 12. To solve for side a, we can use the Law of Cosines, which is represented by the equation:
c² = a² + b² - 2ab cos(y)
In this triangle, angle y corresponds to angle A, side a is opposite angle A, side b is known to us, and side c is known. We rearrange the formula to solve for a:
a² = c² - b² + 2bc cos(A)
Plugging in our known values, we get:
a² = 12² - 19² + 2(19)(12) cos(15°)
To solve for a, we take the square root of both sides after calculating the right side of the equation.
Using a calculator, we find the length of side a to be approximately 16.9 to the nearest tenth. So, the correct answer is B) 16.9.