Math Problem Statement

Find the angle x in the given right triangle with the adjacent side labeled as 3.25 units and the opposite side labeled as 6 units.

Solution

This is a right triangle where:

  • The adjacent side to angle xx is labeled as 3.25 units,
  • The opposite side to angle xx is labeled as 6 units,
  • The hypotenuse is not given but can be calculated if needed.

We can find angle xx using the tangent function, which is defined as:

tan(x)=oppositeadjacent=63.25\tan(x) = \frac{\text{opposite}}{\text{adjacent}} = \frac{6}{3.25}

Let me calculate xx.The angle xx is approximately 61.5661.56^\circ.

Would you like further details or have any questions about this?

Here are five related questions:

  1. How can we calculate the hypotenuse using the Pythagorean theorem?
  2. What is the sine of angle xx based on the triangle's sides?
  3. How would the value of xx change if the opposite side were longer?
  4. Can we calculate the area of this triangle using the given sides?
  5. How can we determine the other acute angle in this triangle?

Tip: When working with right triangles, trigonometric functions like sine, cosine, and tangent are useful to find missing angles and side lengths.

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Right Triangles

Formulas

tan(x) = opposite / adjacent
Pythagorean Theorem

Theorems

Trigonometric Ratios

Suitable Grade Level

Grades 9-12