Questions: Solve the following triangle. A=20°, B=20°, c=9 C ≈ (Simplify your answer.) a ≈ (Type an integer or decimal rounded to two decimal places as needed.) b ≈ (Type an integer or decimal rounded to two decimal places as needed.)

Solution Steps

To solve the given triangle, we can use the Law of Sines and the fact that the sum of angles in a triangle is 180 degrees. First, calculate angle C using the angle sum property. Then, apply the Law of Sines to find the lengths of sides a and b.

Using the angle sum property of triangles, we find angle \( C \) as follows: \[ C = 180^\circ - A - B = 180^\circ - 20^\circ - 20^\circ = 140^\circ \]

We can use the Law of Sines to find the lengths of sides \( a \) and \( b \): \[ \frac{a}{\sin A} = \frac{c}{\sin C} \quad \text{and} \quad \frac{b}{\sin B} = \frac{c}{\sin C} \]

Substituting the known values into the equations: \[ a = \frac{c \cdot \sin A}{\sin C} = \frac{9 \cdot \sin(20^\circ)}{\sin(140^\circ)} \approx 4.7888 \] \[ b = \frac{c \cdot \sin B}{\sin C} = \frac{9 \cdot \sin(20^\circ)}{\sin(140^\circ)} \approx 4.7888 \]

Final Answer