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 xx in the triangle using the tangent function. Here's the solution:

The equation provided is:

tan(x)=68.\tan(x) = \frac{6}{8}.

To solve for xx, we use the inverse tangent function (tan1\tan^{-1}):

x=tan1(68).x = \tan^{-1}\left(\frac{6}{8}\right).

Step 1: Simplify the fraction (if needed)

68=0.75\frac{6}{8} = 0.75

Step 2: Calculate the inverse tangent

Use a calculator or software to find: x=tan1(0.75)x = \tan^{-1}(0.75)

On most calculators: x36.87x \approx 36.87^\circ

Step 3: Round to the nearest hundredth

x36.87x \approx 36.87^\circ

Thus, the value of xx is 36.87 degrees.


Would you like further details or explanations? Below are some questions that can expand on this problem:

  1. What is the significance of the tangent function in trigonometry?
  2. How do you determine which trigonometric function to use when solving triangles?
  3. Can you solve for the other angles of this triangle using trigonometric functions?
  4. How would this solution change if the triangle dimensions were different?
  5. 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