https://file.aiquickdraw.com/mathbot/file/17255701353908sc2i0jc.jpg

Let's solve the problems in the given image step by step.

### Problem (a)
For the first triangle, we have:
- It is a 45°-45°-90° triangle.
- One leg is 3 units, and we need to find the hypotenuse \( d \).

In a 45°-45°-90° triangle, the hypotenuse is \( \sqrt{2} \) times the length of each leg. So:

\[
d = 3 \times \sqrt{2} \approx 3 \times 1.414 \approx 4.2
\]

So, \( d \approx 4.2 \).

### Problem (b)
For the second triangle, we have:
- It is a 30°-60°-90° triangle.
- The side opposite the 30° angle is 4 units, and we need to find the hypotenuse \( a \).

In a 30°-60°-90° triangle, the hypotenuse is twice the length of the side opposite the 30° angle. So:

\[
a = 2 \times 4 = 8
\]

So, \( a = 8 \).

### Answers
(a) \( d \approx 4.2 \)  
(b) \( a = 8 \)

Would you like more details or have any questions?

Here are some related questions:
1. How do you determine the hypotenuse in a 45°-45°-90° triangle if only one leg is given?
2. What is the relationship between the sides of a 30°-60°-90° triangle?
3. How can the Pythagorean theorem be applied to find missing sides in right triangles?
4. How do you round answers to the nearest tenth in mathematical calculations?
5. What are the other common special right triangles and their properties?

**Tip:** For 45°-45°-90° triangles, remember the sides have a ratio of 1:1:√2, and for 30°-60°-90° triangles, the ratio is 1:√3:2.

For the right triangles below, find the values of the side lengths d and a. Round your answers to the nearest tenth.

Discover how to calculate the hypotenuse in special right triangles with angles of 45° and 30°. This guide provides step-by-step solutions for finding side lengths in 45°-45°-90° and 30°-60°-90° triangles, essential for high school geometry and trigonometry.

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