Solve the right triangle.

bequals=1.461.46   

cequals=4.234.23

...

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Part 1

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Part 1

Use the values of b and c to find the value of a.

aalmost equals≈enter your response here

To solve the right triangle given the values:

- \( b = 1.46 \)
- \( c = 4.23 \) (hypotenuse)

we need to find the value of side \( a \).

### Step 1: Apply the Pythagorean Theorem

For a right triangle, the Pythagorean theorem is:

\[
a^2 + b^2 = c^2
\]

Substitute the given values for \( b \) and \( c \):

\[
a^2 + 1.46^2 = 4.23^2
\]

Calculate \( 1.46^2 \) and \( 4.23^2 \):

\[
a^2 + 2.1316 = 17.8929
\]

Solve for \( a^2 \):

\[
a^2 = 17.8929 - 2.1316
\]

\[
a^2 = 15.7613
\]

Take the square root to find \( a \):

\[
a = \sqrt{15.7613}
\]

\[
a \approx 3.97
\]

### Final Answer

- \( a \approx 3.97 \)

Would you like more details or have any questions?

### Related Questions:

1. How can you find the angles in a right triangle using trigonometric ratios?
2. What is the cosine rule, and when is it used?
3. How do you determine the area of a right triangle given two sides?
4. How can you verify the results using a different trigonometric method?
5. What are the properties of a 45-45-90 right triangle?

**Tip:** Make sure to double-check your calculations for accuracy, especially when working with decimals.

Learn how to solve a right triangle given the sides b = 1.46 and c = 4.23 using the Pythagorean Theorem. Detailed step-by-step solution provided. Suitable for high school students.

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