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To solve this problem, we need to find the lengths of the adjacent and opposite sides of a right triangle where:

- The hypotenuse is 92,900,000.
- One angle is 90° (right angle).
- Another angle is 47°.

We can use trigonometric ratios to solve for the adjacent and opposite sides. Let’s denote:

- \( \theta = 47^\circ \) (the given angle).
- Hypotenuse (\( h \)) = 92,900,000.

### Step 1: Calculate the opposite side
The sine function relates the opposite side to the hypotenuse:
\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}
\]
\[
\text{opposite} = \sin(47^\circ) \times 92,900,000
\]

### Step 2: Calculate the adjacent side
The cosine function relates the adjacent side to the hypotenuse:
\[
\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}
\]
\[
\text{adjacent} = \cos(47^\circ) \times 92,900,000
\]

Let me calculate these values for you.The lengths of the sides are:

- **Opposite side:** 67,942,758.88 units
- **Adjacent side:** 63,357,647.65 units

These values were calculated using the trigonometric relationships for sine and cosine based on the given angle and hypotenuse.

Would you like further details, or do you have any questions?

Here are five related questions:
1. How would the results change if the given angle were different, say 30°?
2. What are the implications of using degrees versus radians in trigonometric calculations?
3. How can we find the area of this right triangle using the calculated sides?
4. What if we were given the lengths of the sides instead of the angle and needed to find the angles?
5. How can trigonometric identities be used to verify these calculations?

**Tip:** Always ensure your calculator is set to the correct mode (degrees or radians) to match the problem’s units for angle measurements.

Find the adjacent and opposite sides of a right triangle if the hypotenuse is 92,900,000 and one of the angles is 90 and another is 47.

Learn how to calculate the adjacent and opposite sides of a right triangle with a hypotenuse of 92,900,000 units and a 47° angle using trigonometric functions. This problem covers core trigonometric concepts suitable for students in Grades 9-12.

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