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We are given a right triangle with a base of 15 cm, an angle of 38°, and an area of 80 cm². The hypotenuse is marked as \( m \), and the height is labeled as \( h \).

### Step-by-Step Solution:

1. **Formula for the area of a triangle:**
   The area of a triangle is given by:
   \[
   \text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
   \]
   Substituting the known values:
   \[
   80 = \frac{1}{2} \times 15 \times h
   \]
   Solving for \( h \):
   \[
   80 = 7.5 \times h \quad \Rightarrow \quad h = \frac{80}{7.5} = 10.67 \, \text{cm}
   \]

2. **Relating height \( h \) and hypotenuse \( m \):**
   Using trigonometry, the sine of 38° is:
   \[
   \sin(38^\circ) = \frac{h}{m}
   \]
   Substituting the value of \( h \):
   \[
   \sin(38^\circ) = \frac{10.67}{m}
   \]
   Solving for \( m \):
   \[
   m = \frac{10.67}{\sin(38^\circ)}
   \]
   Using \( \sin(38^\circ) \approx 0.6157 \):
   \[
   m = \frac{10.67}{0.6157} \approx 17.33 \, \text{cm}
   \]

Thus, the value of \( m \) is approximately **17.33 cm**.

Would you like more details or have any questions?

Here are 5 related questions to further your understanding:
1. How do you calculate the height of a right triangle using trigonometry?
2. Can you find the length of the other side of the triangle using the Pythagorean theorem?
3. What other trigonometric functions can you use in this triangle, and how?
4. How does the area formula change if the triangle is not a right triangle?
5. What other ways can you solve for \( m \) without the area?

**Tip:** Always check if you're using degrees or radians when using trigonometric functions on your calculator!

The area of the triangle above is 80 cm². Calculate the value of m.

Solve for the hypotenuse of a right triangle with a base of 15 cm and an angle of 38°. Given the area of 80 cm², use trigonometry and the area formula to find the length of m. Detailed steps for Grades 9-10.

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