Questions: Solve the triangle. B=53° (Do not round until the final answer. Then round to the nearest degree as needed.) b ≈ (Do not round until the final answer. Then round to the nearest tenth as needed.) c ≈ (Do not round until the final answer. Then round to the nearest tenth as needed.)

Solve the triangle.

Find angle \(A\).

The sum of the angles in a triangle is \(180^\circ\). We are given \(C = 87^\circ\) and \(B = 40^\circ\). Therefore, \(A = 180^\circ - 87^\circ - 40^\circ = 53^\circ\).

Find side \(b\).

Using the Law of Sines, we have \(\frac{b}{\sin B} = \frac{a}{\sin A}\). Plugging in the given values, we get \(\frac{b}{\sin 40^\circ} = \frac{9}{\sin 53^\circ}\). \(b = \frac{9 \sin 40^\circ}{\sin 53^\circ} \approx \frac{9 \times 0.6428}{0.7986} \approx 7.2\).

Find side \(c\).

Using the Law of Sines, we have \(\frac{c}{\sin C} = \frac{a}{\sin A}\). Plugging in the given values, we get \(\frac{c}{\sin 87^\circ} = \frac{9}{\sin 53^\circ}\). \(c = \frac{9 \sin 87^\circ}{\sin 53^\circ} \approx \frac{9 \times 0.9986}{0.7986} \approx 11.3\).

\(A = 53^\circ\), \(b \approx 7.2\), \(c \approx 11.3\).

\(A = \boxed{53^\circ}\) \(b \approx \boxed{7.2}\) \(c \approx \boxed{11.3}\)