Questions: Solve the right triangle. Round your answers to the nearest tenth.

Transcript text: Solve the right triangle. Round your answers to the nearest tenth.

Solution

Solution Steps

Step 1: Find angle A

The sum of the angles in a triangle is 180°. We are given a right triangle, so one angle is 90° and another is 50°. Therefore, angle A is: \(A = 180° - 90° - 50° = 40°\)

Step 2: Find side a

We can use the sine function to find side a. \(\sin(50°) = \frac{a}{20}\) \(a = 20 \sin(50°)\) \(a \approx 20 \times 0.766 = 15.32\) Rounding to the nearest tenth, we get \(a \approx 15.3\).

Step 3: Find side b

We can use the cosine function to find side b. \(\cos(50°) = \frac{b}{20}\) \(b = 20 \cos(50°)\) \(b \approx 20 \times 0.643 = 12.86\) Rounding to the nearest tenth, we get \(b \approx 12.9\).

Final Answer

\(A = 40°\) \(a \approx \boxed{15.3}\) \(b \approx \boxed{12.9}\)

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