Math Problem Statement
Solution
The goal here is to find the missing angles in each triangle using the provided side lengths. For triangles where two sides and an angle are known, we'll often use trigonometric laws, like the Law of Cosines or Law of Sines, depending on the given values.
Let's start by solving each triangle step by step:
1. Triangle 1:
Given sides:
We can use the Cosine Rule to find angle .
Cosine rule: where .
Substitute the values to solve for .
2. Triangle 2:
Given sides:
Again, we use the Cosine Rule to find angle .
where .
3. Triangle 3:
Given sides:
Use the Cosine Rule to find angle .
4. Triangle 4:
Given sides:
Find angle using the Cosine Rule.
5. Triangle 5:
Given sides:
Use the Cosine Rule to find angle
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Triangles
Cosine Rule
Formulas
Cosine Rule: cos(C) = (a^2 + b^2 - c^2) / 2ab
Sum of angles in a triangle: 180°
Theorems
Cosine Rule
Suitable Grade Level
Grades 9-12
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