Math Problem Statement
Solution
We are tasked with finding side of a triangle given the following:
- ,
- ,
- Side .
Solution:
-
Find the third angle :
-
Apply the Law of Sines: The Law of Sines states: Using , we solve for :
-
Substitute the known values:
-
Calculate the sines and solve: Using a calculator:
-
Round to the nearest whole number:
Final Answer:
The side is approximately 15.
Would you like a detailed explanation of any step or further questions?
Here are five related questions to consider:
- How is the Law of Sines used in non-right triangles?
- Why do we need to find the missing angle in a triangle before applying trigonometric laws?
- What other methods can be used to solve triangles (e.g., Law of Cosines)?
- Can the Law of Sines determine whether a triangle is obtuse, acute, or right?
- What happens when given a side and two angles (SAA) in a triangle?
Tip: Always ensure your calculator is set to degrees when solving angle-related problems.
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Triangles
Law of Sines
Formulas
Law of Sines: a/sin(A) = b/sin(B) = c/sin(C)
Theorems
Law of Sines
Suitable Grade Level
Grades 10-12
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