Math Problem Statement
Solution
To solve for , the missing side of the triangle, we apply trigonometry. Here's the reasoning:
Step 1: Identify given information
- The triangle involves the given side , which is adjacent to the angle .
- The unknown side is opposite to the angle .
- The trigonometric function that relates the opposite and adjacent sides is the tangent function:
Step 2: Write the tangent equation
Step 3: Solve for
Rearrange the equation to isolate :
Step 4: Calculate the value
Using a calculator:
Final Answer:
The value of , rounded to the nearest tenth, is:
Would you like a detailed explanation of any specific step or concept?
5 Related Questions:
- How do we choose which trigonometric function to use in different triangle problems?
- What other ways can we solve for if additional sides or angles were provided?
- Can this triangle be solved using the Pythagorean theorem?
- How is the tangent function derived in trigonometry?
- What are some practical applications of this problem-solving approach?
Tip:
Always double-check whether your calculator is in degree mode when working with angles given in degrees.
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Tangent Function
Solving Right Triangles
Formulas
tan(angle) = opposite/adjacent
x = adjacent * tan(angle)
Theorems
Trigonometric Functions in Right Triangles
Suitable Grade Level
Grades 9-12
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