Final answer:
To find the missing side a in a non-right triangle, use the Law of Sines. Calculate the third angle by subtracting the other two angles from 180°, and then set up the proportion of the sine of angle A to side a equal to the sine of angle C to side c. Solve for a and round to the nearest tenth.
Step-by-step explanation:
To find the missing side a when given one side, c, and two angles, A and B, in a non-right triangle, you can use the Law of Sines. The Law of Sines states that the ratio of the length of a side to the sine of its opposite angle is constant for all sides and angles in a triangle:
a/sin(A) = b/sin(B) = c/sin(C)
In this scenario:
A = 45°
B = 100°
c = 15
To find C, the third angle, we use the fact that the sum of angles in a triangle is 180°:
C = 180° - A - B
C = 180° - 45° - 100°
C = 35°
Then, using the Law of Sines, we solve for a:
c/sin(C) = a/sin(A)
Now, plug in the known values:
15/sin(35°) = a/sin(45°)
We solve for a:
a = (15 * sin(45°)) / sin(35°)
By calculating this on a calculator, we can round the result to the nearest tenth.