1. **Problem Statement:** We have a triangle with one angle measuring 87° and two sides labeled as 19a and 12a. We need to find the value of the variable $a$ representing an angle in degrees. 2. **Understanding the Triangle:** The sides 19a and 12a are opposite to certain angles. Since the angle given is 87°, and the sides are proportional to $a$, we can use the Law of Sines to find $a$. 3. **Law of Sines Formula:** $$\frac{\text{side}_1}{\sin(\text{angle}_1)} = \frac{\text{side}_2}{\sin(\text{angle}_2)}$$ 4. **Assigning Values:** - Side opposite 87° is $19a$ - Side opposite angle $a$ is $12a$ 5. **Set up the equation:** $$\frac{19a}{\sin(87^\circ)} = \frac{12a}{\sin(a)}$$ 6. **Simplify the equation:** Since $a$ is a common factor on both sides, it cancels out: $$\frac{19}{\sin(87^\circ)} = \frac{12}{\sin(a)}$$ 7. **Solve for $\sin(a)$:** $$\sin(a) = \frac{12 \times \sin(87^\circ)}{19}$$ 8. **Calculate $\sin(87^\circ)$:** $$\sin(87^\circ) \approx 0.9986$$ 9. **Calculate $\sin(a)$:** $$\sin(a) = \frac{12 \times 0.9986}{19} \approx \frac{11.9832}{19} \approx 0.6307$$ 10. **Find angle $a$:** $$a = \sin^{-1}(0.6307) \approx 39.2^\circ$$ **Final answer:** $$a \approx 39.2^\circ$$