Math Problem Statement
Solution
To find the measure of angle A in the given right triangle, we can use trigonometric ratios and the inverse trigonometric functions. Here, we have the sides of the triangle:
- The side opposite to angle A is 38 m.
- The adjacent side to angle A is 48 m.
The tangent function (tan) is suitable for this case since it relates the opposite side to the adjacent side:
Now, to find angle A, we use the inverse tangent (arctan or tan⁻¹):
Using a calculator:
So, the measure of angle A is approximately 38.56 degrees.
Let me know if you'd like more details or have any further questions!
Here are 5 related questions for further exploration:
- How would the result change if the opposite and adjacent sides were switched?
- What is the difference between the sine and cosine functions in trigonometry?
- How can we calculate the length of the hypotenuse in this triangle?
- How does the inverse sine function differ from the inverse tangent function?
- What is the sum of the interior angles of a right triangle, and how can we use this information?
Tip: When using inverse trigonometric functions, always make sure your calculator is set to the correct mode (degrees or radians) based on the problem.
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Right Triangles
Inverse Trigonometric Functions
Formulas
tan(A) = opposite/adjacent
A = tan⁻¹(opposite/adjacent)
Theorems
Pythagorean Theorem indirectly relates to hypotenuse calculation if needed
Suitable Grade Level
Grades 9-12
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