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From the image, we see a right triangle with the following dataFrom the image, we see a right triangle with the following 

- Side \( a = 14.3 \)
- Angle \( B = 50^\circ \)
- We need to find the length of side \( c \).

To find the side \( c \), we can use the **trigonometric ratio of cosine** since the adjacent side (to angle \( B \)) is given (side \( a \)):

\[
\cos(B) = \frac{a}{c}
\]

Rearranging this equation to solve for \( c \):

\[
c = \frac{a}{\cos(B)}
\]

Now, substituting the values:

\[
c = \frac{14.3}{\cos(50^\circ)}
\]

Let's calculate the value of \( c \).The length of side \( c \) is approximately 22.25 units.

Would you like more details or have any questions?

Here are 5 related questions that might expand your understanding:
1. How can you use the sine and tangent ratios to find other sides of the triangle?
2. How would the triangle change if angle \( B \) were increased or decreased?
3. How can we verify the result using the Pythagorean theorem?
4. What is the relationship between angle \( B \) and angle \( A \) in the triangle?
5. Can you calculate the area of this triangle with the given data?

**Tip:** In right-angled triangles, the cosine function is often used when dealing with the adjacent side and the hypotenuse, while sine deals with the opposite side and hypotenuse.

Given a right triangle with side a = 14.3, angle B = 50°, and we need to find the hypotenuse c.

Learn how to solve for the hypotenuse c in a right triangle using trigonometry, given angle B = 50° and side a = 14.3. This solution involves using the cosine function and the basic principles of right triangle trigonometry. Suitable for students in Grades 9-11.

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