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The given triangle has the following details:
- Hypotenuse (\( c \)) = 17
- One angle = 10°
- \( a \) is the side opposite the 10° angle.
- \( b \) is the adjacent side (opposite angle \( B \)).

We can use trigonometric functions to solve for \( a \) and \( b \).

1. **Finding \( a \) (opposite side):**

Using the sine function:
\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \quad \Rightarrow \quad a = \text{hypotenuse} \times \sin(10^\circ)
\]

2. **Finding \( b \) (adjacent side):**

Using the cosine function:
\[
\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \quad \Rightarrow \quad b = \text{hypotenuse} \times \cos(10^\circ)
\]

I'll calculate these values now.The values of the sides are:

- \( a \approx 2.9520 \)
- \( b \approx 16.7417 \)

Would you like more details or have any questions?

Here are some related questions for further exploration:
1. How would the values of \( a \) and \( b \) change if the angle increased to 20°?
2. How does changing the length of the hypotenuse affect the values of \( a \) and \( b \)?
3. Can you use tangent to calculate either side in this problem?
4. What is the relationship between sine and cosine for complementary angles in this context?
5. How would you solve this problem using the Pythagorean theorem after finding one side?

**Tip:** When solving right triangles, always check if you can use the sine, cosine, or tangent based on the information provided.

Use a calculator, spreadsheet, or another tool to solve for the unknown sides of the given right triangle. The length of the hypotenuse is 17. a is the length of the side opposite the 10° angle and b is the length of the side opposite angle B. Round your answers to four decimal places.

Discover how to use trigonometry to calculate the sides of a right triangle when the hypotenuse and one angle are known. This guide provides step-by-step instructions on applying sine and cosine functions to find the lengths of sides opposite and adjacent to a 10° angle in a triangle with a hypotenuse of 17.

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