Questions: Solve the triangle.

Solve the triangle.
Transcript text: Solve the triangle.
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Solution

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Solution Steps

Step 1: Find angle B

The sum of the angles in a triangle is 180°. We are given angle C = 90° and angle A = 50°. Therefore, angle B = 180° - 90° - 50° = 40°.

Step 2: Find side c

We can use the trigonometric function cosine to relate side c to side b (which is given as 8). Cosine of an angle is equal to the adjacent side divided by the hypotenuse. In our case, cos(50°) = c/8. Therefore, c = 8 * cos(50°) ≈ 5.14.

Step 3: Find side a

We can use the trigonometric function sine to find side a. Sine of an angle is equal to the opposite side divided by the hypotenuse. In our case, sin(50°) = a/8. Therefore, a = 8 * sin(50°) ≈ 6.13.

Final Answer:

Angle B = 40°, side c ≈ 5.14, side a ≈ 6.13

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