In ΔKLM, *l* = 4.1 cm, *m* = 2.4 cm and ∠K=97°. Find the area of ΔKLM, *to the nearest 10th of a square centimeter*.

To find the area of triangle \( \Delta KLM \), we use the formula:

\[
\text{Area} = \frac{1}{2} \times l \times m \times \sin(\theta)
\]

where:
- \( l = 4.1 \) cm
- \( m = 2.4 \) cm
- \( \theta = \angle K = 97^\circ \)

### Step 1: Calculate \( \sin(97^\circ) \)
Since \( 97^\circ \) is slightly greater than \( 90^\circ \), we can directly use its sine value:
\[
\sin(97^\circ) \approx 0.9986
\]

### Step 2: Plug in the values
\[
\text{Area} \approx \frac{1}{2} \times 4.1 \times 2.4 \times 0.9986
\]

### Step 3: Calculate the area
\[
\text{Area} \approx \frac{1}{2} \times 4.1 \times 2.4 \times 0.9986 \approx 4.917 \text{ square centimeters}
\]

Rounding to the nearest 10th, the area of \( \Delta KLM \) is approximately **4.9 square centimeters**.

Do you want details or have any questions?

Here are 5 related questions you might be interested in:

1. How would the area change if \( \angle K \) was an acute angle?
2. What is the relationship between sine and cosine for angles greater than 90°?
3. How can you find the length of side \( k \) using the Law of Cosines?
4. How do you determine the height of \( \Delta KLM \) relative to side \( l \)?
5. What would be the area if \( \angle K \) were exactly \( 90^\circ \)?

**Tip:** For angles close to \( 90^\circ \), the sine value is close to 1, making the area formula simple to approximate.

Learn how to calculate the area of triangle KLM with side lengths l = 4.1 cm, m = 2.4 cm, and angle K = 97° using the sine formula. This problem covers basic trigonometric concepts and the application of trigonometric ratios in geometry. Suitable for students in Grades 9-10.

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