Questions: Solve the right triangle. Round your answers to the nearest tenth. A=40° b= c=

Solve the right triangle. Round your answers to the nearest tenth. A=40° b= c=
Transcript text: Solve the right triangle. Round your answers to the nearest tenth. \[ \begin{array}{l} A=40^{\circ} \\ b=\square \\ c=\square \end{array} \]
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Solution

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Solution Steps

Step 1: Find Angle A

Since it's a right triangle, one angle is 90°. We are given another angle as 50°. The sum of angles in a triangle is 180°. Therefore, angle A = 180° - 90° - 50° = 40°.

Step 2: Find side c

We can use the sine function to find side c. sin(50°) = opposite/hypotenuse = 19/c. Therefore, c = 19/sin(50°) ≈ 24.8.

Step 3: Find side b

We can use the cosine function to find side b. cos(50°) = adjacent/hypotenuse = b/c. We already calculated c ≈ 24.8. Therefore, b = 24.8 * cos(50°) ≈ 15.9.

Final Answer

A = 40° b ≈ 15.9 c ≈ 24.8

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