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To solve for \(\angle A\) in the triangle with sides \(a = 22\), \(b = 17\), and \(c = 15\), we can use the **Law of Cosines**.

The Law of Cosines states that for any triangle:

\[
\cos A = \frac{b^2 + c^2 - a^2}{2bc}
\]

Substituting the given values \(a = 22\), \(b = 17\), and \(c = 15\):

\[
\cos A = \frac{17^2 + 15^2 - 22^2}{2 \times 17 \times 15}
\]

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Here are a few related questions you might be interested in:

1. How can the Law of Sines help solve triangles?
2. What is the difference between the Law of Cosines and the Pythagorean Theorem?
3. How do we find other angles in a triangle after one angle is known?
4. What are some real-life applications of the Law of Cosines?
5. How do we determine if a triangle is acute, obtuse, or right based on its angles?

**Tip:** When dealing with triangles, always check whether a triangle is valid (sum of any two sides must be greater than the third).

In the triangle below, a=22, b=17, and c=15. Find the measure of angle A to the nearest tenth.

Learn how to solve for angle A in a triangle with sides a=22, b=17, and c=15 using the Law of Cosines. This geometry and trigonometry problem applies key mathematical concepts and formulas to find the angle to the nearest tenth. Suitable for high school students in Grades 10-12.

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