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This problem involves a right triangle \(ABC\) with angle \(C = 90^\circ\). You are given the lengths of sides \(a = 44.7\) inches and \(b = 35.8\) inches, where \(a\) and \(b\) represent the two legs of the right triangle. The goal is to find the measure of angle \(B\).

We can use the following trigonometric relation for right triangles:

\[
\tan(B) = \frac{a}{b}
\]

Now, solving for \(B\):

\[
B = \tan^{-1}\left( \frac{a}{b} \right)
\]

Let me calculate that.The measure of angle \( B \) is approximately \( 51.3^\circ \).

Would you like any further details or have any additional questions?

Here are 5 related questions to explore:
1. How can you calculate angle \( A \) in this right triangle?
2. What is the hypotenuse of the triangle given sides \( a \) and \( b \)?
3. How would you solve for angle \( B \) if different side lengths were given?
4. Can you apply the Law of Cosines to this triangle even though it is a right triangle?
5. What would change if angle \( B \) were given instead of the side lengths?

**Tip**: Always double-check trigonometric ratios by ensuring you're using the right function for the given information (e.g., \(\sin\), \(\cos\), \(\tan\)).

If a = 44.7 inches and b = 35.8 inches, find B in a right triangle ABC with C = 90°.

Learn how to calculate the angle B in a right triangle ABC, where sides a = 44.7 inches and b = 35.8 inches, using trigonometric formulas. This problem introduces key concepts in trigonometry and is suitable for students in Grades 9-12.

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