solve unknown sides of right triangle. the length of the hypotenuse is 11. a is the lenght of the side opposite the 10degree angle and b is the length of the side opposite angle B. round answers to 4 decimals 

To solve the unknown sides of a right triangle, we can use trigonometric relationships based on the given angles and the hypotenuse. Let’s summarize the given information:

- Hypotenuse \( c = 11 \)
- Angle \( A = 10^\circ \) (opposite to side \( a \))
- Angle \( B = 90^\circ - 10^\circ = 80^\circ \) (opposite to side \( b \))

We can use the following trigonometric formulas:

1. **For side \( a \)** (opposite to angle \( A \)):
   \[
   a = c \cdot \sin(A)
   \]
   \[
   a = 11 \cdot \sin(10^\circ)
   \]

2. **For side \( b \)** (opposite to angle \( B \)):
   \[
   b = c \cdot \sin(B)
   \]
   \[
   b = 11 \cdot \sin(80^\circ)
   \]

Now, let me calculate these values for you.The lengths of the unknown sides of the right triangle are:

- \( a = 1.9101 \) (opposite the 10° angle)
- \( b = 10.8329 \) (opposite the 80° angle)

Would you like further clarification or details on the method? Here are five related questions to extend your understanding:

1. How do you determine the adjacent side using cosine in a right triangle?
2. What would the side lengths be if the hypotenuse were 15 instead of 11?
3. How can the Pythagorean theorem verify the results of trigonometric methods?
4. What are other trigonometric functions that could be used to solve for sides of a right triangle?
5. How do you solve right triangles if both legs are known but not the angles?

**Tip:** Always double-check whether your calculator is set to degrees or radians when solving trigonometric problems!

solve unknown sides of right triangle. the length of the hypotenuse is 11. a is the length of the side opposite the 10degree angle and b is the length of the side opposite angle B. round answers to 4 decimals

Learn how to solve for the unknown sides of a right triangle with a hypotenuse of 11 and angles 10° and 80°. Using trigonometric formulas, find side lengths accurate to 4 decimal places. Perfect for students in Grades 9-10 exploring right triangle trigonometry.

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