Questions: Solve the right triangle. Round your answers to the nearest tenth. A= ° a= b=

Solution Steps

Since the sum of angles in a triangle is 180 degrees and we know one angle is 90 degrees and another is 50 degrees, we can find angle A. \[ A = 180^\circ - 90^\circ - 50^\circ = 40^\circ \]

Using the sine function for angle 50 degrees: \[ \sin(50^\circ) = \frac{a}{21} \] \[ a = 21 \times \sin(50^\circ) \] \[ a \approx 21 \times 0.766 = 16.1 \]

Using the cosine function for angle 50 degrees: \[ \cos(50^\circ) = \frac{b}{21} \] \[ b = 21 \times \cos(50^\circ) \] \[ b \approx 21 \times 0.643 = 13.5 \]

Final Answer