Questions: Consider a triangle ABC like the one below. Suppose that a = 26, b = 57, and c = 73. (The figure is not drawn to scale.) Solve the triangle. Carry your intermediate computations to at least four decimal places, and round your answers to the nearest tenth. If there is more than one solution, use the button labeled "or". A = , B = , C =

Consider a triangle ABC like the one below. Suppose that a = 26, b = 57, and c = 73. (The figure is not drawn to scale.) Solve the triangle.

Carry your intermediate computations to at least four decimal places, and round your answers to the nearest tenth.

If there is more than one solution, use the button labeled "or".

A = , B = , C =

Transcript text: Consider a triangle ABC like the one below. Suppose that a = 26, b = 57, and c = 73. (The figure is not drawn to scale.) Solve the triangle. Carry your intermediate computations to at least four decimal places, and round your answers to the nearest tenth. If there is more than one solution, use the button labeled "or". A = $\square$, B = $\square$, C = $\square$

Solution

Solution Steps

Step 1: Find angle C using the Law of Cosines

The Law of Cosines states: c² = a² + b² - 2ab * cos(C)

Plugging in the given values: 73² = 26² + 57² - 2 * 26 * 57 * cos(C)

5329 = 676 + 3249 - 2964 * cos(C)

5329 = 3925 - 2964 * cos(C)

1404 = -2964 * cos(C)

cos(C) = -1404/2964

C = arccos(-1404/2964)

C ≈ 118.1°

Step 2: Find angle A using the Law of Sines

The Law of Sines states: a/sin(A) = b/sin(B) = c/sin(C)

Using a/sin(A) = c/sin(C):

26/sin(A) = 73/sin(118.1°)

sin(A) = 26 * sin(118.1°)/73

sin(A) ≈ 0.3184

A = arcsin(0.3184)

A ≈ 18.6°

Step 3: Find angle B

The sum of angles in a triangle is 180°.

A + B + C = 180°

18.6° + B + 118.1° = 180°

B = 180° - 18.6° - 118.1°

B ≈ 43.3°

Final Answer

A ≈ 18.6°, B ≈ 43.3°, C ≈ 118.1°

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