Final answer:
To find the length of side x in a triangle with side length 2.4 and angle measure 39 degrees, we can use the Law of Sines. By setting up a proportion and solving for x, we can find its length.
Step-by-step explanation:
To find the length of side x in a triangle, we can use the Law of Sines. The Law of Sines states that the ratio of each side of a triangle to the sine of its opposite angle is constant. In this case, we have the length of side 2.4 and the measure of angle 39 degrees. Let's label the other two sides as a and b, and their opposite angles as A and B respectively. We can set up the proportion:
2.4 / sin(39°) = x / sin(A)
Solving for x, we can use the sine function and cross-multiplication:
x = (2.4 * sin(A)) / sin(39°)
To find angle A, we can use the fact that the sum of the angles in a triangle is 180 degrees. Let's call angle C the remaining angle. We know that A + B + C = 180°, and we also know that angle B is 39°. Rearranging the equation, we have:
180° - 39° - C = A
Now, we can substitute the value of angle A into the equation for x to find its length.