Math Problem Statement
Solve for x. Given tan(x) = 6/8, find the angle x using the inverse tangent function (tan⁻¹(6/8)). Round to the nearest hundredth.
Solution
This problem asks you to solve for the angle in the triangle using the tangent function. Here's the solution:
The equation provided is:
To solve for , we use the inverse tangent function ():
Step 1: Simplify the fraction (if needed)
Step 2: Calculate the inverse tangent
Use a calculator or software to find:
On most calculators:
Step 3: Round to the nearest hundredth
Thus, the value of is 36.87 degrees.
Would you like further details or explanations? Below are some questions that can expand on this problem:
- What is the significance of the tangent function in trigonometry?
- How do you determine which trigonometric function to use when solving triangles?
- Can you solve for the other angles of this triangle using trigonometric functions?
- How would this solution change if the triangle dimensions were different?
- How can you verify the answer using another trigonometric property?
Tip: Always double-check your calculator is set to the correct mode (degrees or radians) when solving trigonometric problems.
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Inverse Trigonometric Functions
Right Triangle Ratios
Formulas
tan(x) = opposite / adjacent
x = tan⁻¹(opposite / adjacent)
Theorems
Definition of Tangent Function
Suitable Grade Level
Grades 9-12