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The problem involves a right triangle where you are likely asked to find an unknown angle or side, using trigonometric relationships. In the given image, the triangle has a hypotenuse labeled as \( d \) and a leg labeled as 41. The angle adjacent to the leg of 41 is marked as \( \theta \).

To solve for \( \theta \), we can use the cosine function because the cosine of an angle in a right triangle is defined as the ratio of the adjacent side to the hypotenuse:

\[
\cos(\theta) = \frac{\text{adjacent side}}{\text{hypotenuse}} = \frac{41}{d}
\]

Given that \( d = 47 \) (as shown in the image), we can calculate \( \theta \) using the following steps:

\[
\cos(\theta) = \frac{41}{47}
\]

First, let's calculate this value:

\[
\cos(\theta) \approx \frac{41}{47} \approx 0.87234
\]

Next, to find \( \theta \), take the arccosine (inverse cosine) of 0.87234:

\[
\theta = \cos^{-1}(0.87234) \approx 29.51^\circ
\]

Thus, the angle \( \theta \) is approximately \( 29.51^\circ \).

Would you like more details or have any questions?

Here are five related questions for further exploration:
1. What is the sine of the angle \( \theta \) in this triangle?
2. How would you calculate the length of the opposite side using \( \theta \) and the hypotenuse?
3. If the hypotenuse were 50 instead of 47, what would \( \theta \) be?
4. Can you calculate the area of this right triangle?
5. How does the angle \( \theta \) change as the adjacent side length increases?

**Tip:** When working with trigonometric functions, remember that the arccosine function returns an angle in degrees or radians, depending on the calculator setting. Always ensure you're interpreting the output in the correct units.

Find the angle θ in a right triangle with a hypotenuse of 47 and an adjacent side of 41.

Learn how to find the angle θ in a right triangle where the hypotenuse is 47 and the adjacent side is 41. This problem covers trigonometric concepts, including cosine and inverse cosine functions. Suitable for students in Grades 9-12.

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