Math Problem Statement

Find x. Round your answer to the nearest tenth of a degree.

Solution

To find the angle xx in the given right triangle, we can use the trigonometric function tangent, defined as:

tan(θ)=oppositeadjacent\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}

Here, the side opposite to angle xx is 15, and the side adjacent to xx is 21. Therefore, we have:

tan(x)=1521\tan(x) = \frac{15}{21}

To find xx, we take the arctangent (inverse tangent) of 1521\frac{15}{21}:

x=arctan(1521)x = \arctan\left(\frac{15}{21}\right)

Let's calculate this:

xarctan(0.7143)35.5x \approx \arctan(0.7143) \approx 35.5^\circ

So, x35.5x \approx 35.5^\circ when rounded to the nearest tenth of a degree.

Would you like a more detailed explanation or have any further questions?

Here are some related questions for further exploration:

  1. What is the sine of angle xx in this triangle?
  2. How would you find the hypotenuse using the Pythagorean theorem?
  3. Can you determine the other acute angle in the triangle?
  4. How would the calculation change if the sides were labeled differently?
  5. What other trigonometric functions can be used to find angle xx?

Tip: Always double-check which sides are opposite and adjacent relative to the angle you are finding.

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Right Triangle

Formulas

tan(θ) = opposite / adjacent
arctan(value) = θ

Theorems

Trigonometric Ratios
Inverse Tangent

Suitable Grade Level

Grades 9-10