https://file.aiquickdraw.com/mathbot/file/1729518620392x8r1zbdo.jpg

From the image, we can see a right triangle with the following given information:
- One of the angles is \(62^\circ\).
- The side adjacent to this angle has a length of 15 units.

To find the missing side lengths, we can use trigonometric ratios:
1. **Cosine** function relates the adjacent side and the hypotenuse:
   \[
   \cos(62^\circ) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{15}{\text{hypotenuse}}
   \]
   Rearranging for the hypotenuse:
   \[
   \text{hypotenuse} = \frac{15}{\cos(62^\circ)}
   \]

2. **Sine** function relates the opposite side and the hypotenuse:
   \[
   \sin(62^\circ) = \frac{\text{opposite}}{\text{hypotenuse}}
   \]
   Once we know the hypotenuse, we can use this to find the opposite side:
   \[
   \text{opposite} = \sin(62^\circ) \times \text{hypotenuse}
   \]

Let me compute these values for you.

- \(\cos(62^\circ) \approx 0.4695\)
- Hypotenuse \( = \frac{15}{0.4695} \approx 31.94\)

Now, using the hypotenuse to find the opposite side:
- \(\sin(62^\circ) \approx 0.8829\)
- Opposite side \( = 0.8829 \times 31.94 \approx 28.19\)

So, the hypotenuse is approximately 31.94 units, and the opposite side is approximately 28.19 units.

Would you like more details or have any questions about these calculations?

Here are some related questions to consider:
1. How does the tangent function relate the opposite and adjacent sides?
2. Can you calculate the angle opposite the missing side using another method?
3. How would these results change if the triangle were not a right triangle?
4. Could the Pythagorean theorem also be used to verify the missing side lengths?
5. How would you find the area of this triangle?

**Tip:** When using trigonometric functions, always ensure your calculator is set to the correct mode (degrees or radians).

Calculate the missing lengths of a right triangle with one angle of 62 degrees and an adjacent side length of 15 units.

Learn how to calculate the missing sides of a right triangle with an angle of 62° and adjacent side length of 15 units. This problem involves trigonometric ratios such as sine and cosine to find the hypotenuse and opposite side. Suitable for high school students in Grades 9-12.

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