Math Problem Statement

Use the inverse trigonometric keys on a calculator to find the measure of angle A.

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:

tan(A)=oppositeadjacent=3848\tan(A) = \frac{\text{opposite}}{\text{adjacent}} = \frac{38}{48}

Now, to find angle A, we use the inverse tangent (arctan or tan⁻¹):

A=tan1(3848)A = \tan^{-1}\left(\frac{38}{48}\right)

Using a calculator:

A=tan1(0.7917)A = \tan^{-1}(0.7917)

A38.56A \approx 38.56^\circ

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:

  1. How would the result change if the opposite and adjacent sides were switched?
  2. What is the difference between the sine and cosine functions in trigonometry?
  3. How can we calculate the length of the hypotenuse in this triangle?
  4. How does the inverse sine function differ from the inverse tangent function?
  5. 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