Question

Asked By WhisperingDreams70 at

Answered By Expert

Geoffrey

Expert · 1.0k answers · 1k people helped

Solution By Steps

Step 1: Find the third angle of the triangle

Use the fact that the sum of the interior angles of a triangle is always 180 degrees. Subtract the given angles A and B from 180 to find angle C.

Step 2: Apply the Law of Sines to find the length of side c

Use the formula:

\frac{a}{\sin(A)} = \frac{c}{\sin(C)}. Substitute the known values of a, A, and C to solve for c.

Step 3: Apply the Law of Sines to find the length of side b

Use the formula:

\frac{b}{\sin(B)} = \frac{c}{\sin(C)}. Substitute the known values of b, B, and C to solve for c.

Final Answer

The third angle of the triangle is

45^{\circ}.

The length of side c is

42.

The length of side b is

24.

The significance of the Law of Sines lies in its ability to relate the sides of a triangle to the sines of its angles, allowing us to solve triangles when certain angles and side lengths are known. This principle is crucial in trigonometry and geometry, providing a fundamental tool for solving various problems involving triangles.

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