1. **State the problem:** We have a right triangle with angle B = 63° and angle A = 27° (since the sum of angles in a triangle is 180° and the right angle at C is 90°). 2. **Identify the sides:** $\overline{AB}$ is the hypotenuse, $\overline{AC}$ is the leg opposite angle B, and $\overline{BC}$ is the leg adjacent to angle B. 3. **Use trigonometric ratios:** For angle B, - Opposite side: $\overline{AC}$ - Hypotenuse: $\overline{AB}$ The sine function relates opposite side and hypotenuse: $$\sin(B) = \frac{\overline{AC}}{\overline{AB}}$$ 4. **Express $\overline{AC}$ in terms of $\overline{AB}$:** $$\overline{AC} = \overline{AB} \times \sin(63^\circ)$$ 5. **Use cosine to find the adjacent side $\overline{BC}$:** $$\cos(B) = \frac{\overline{BC}}{\overline{AB}} \implies \overline{BC} = \overline{AB} \times \cos(63^\circ)$$ 6. **Since $\overline{AB}$ is unknown, if given, plug in the value to find $\overline{AC}$ and $\overline{BC}$.** 7. **If $\overline{AB}$ is not given, the missing measurements can be expressed as multiples of $\overline{AB}$:** - $\overline{AC} = \overline{AB} \times 0.8910$ (rounded to 4 decimals) - $\overline{BC} = \overline{AB} \times 0.4539$ (rounded to 4 decimals) **Final answer:** - $\overline{AC} \approx 0.9 \times \overline{AB}$ - $\overline{BC} \approx 0.45 \times \overline{AB}$ If $\overline{AB}$ is provided, multiply to get numeric values rounded to the nearest tenth.