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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