What is the length of the missing leg? If necessary, round to the nearest tenth. c=8.9 b=8.7

To find the length of the missing leg in a right triangle, you can use the Pythagorean theorem:

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

Here, \( c = 8.9 \) (the hypotenuse) and \( b = 8.7 \) (one of the legs). We're looking for the missing leg \( a \).

1. Substitute the known values into the equation:

\[
a^2 + 8.7^2 = 8.9^2
\]

2. Calculate \( 8.7^2 \) and \( 8.9^2 \):

\[
8.7^2 = 75.69
\]
\[
8.9^2 = 79.21
\]

3. Plug these values into the equation:

\[
a^2 + 75.69 = 79.21
\]

4. Subtract 75.69 from both sides to solve for \( a^2 \):

\[
a^2 = 79.21 - 75.69 = 3.52
\]

5. Take the square root of both sides to find \( a \):

\[
a = \sqrt{3.52} \approx 1.876
\]

Rounding to the nearest tenth:

\[
a \approx 1.9
\]

So, the length of the missing leg \( a \) is approximately **1.9**.

Would you like more details or have any questions?

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Here are 8 related questions:
1. How do you apply the Pythagorean theorem to solve for the hypotenuse?
2. What are the conditions for a triangle to be classified as a right triangle?
3. How do you solve for a leg if both legs are unknown, but the hypotenuse is given?
4. What are the implications if the calculated leg length was negative?
5. How does the Pythagorean theorem extend to non-right triangles?
6. Can you use trigonometric ratios to find the missing leg in this case?
7. What is the geometric interpretation of the Pythagorean theorem?
8. How would the problem change if the hypotenuse were not the longest side?

**Tip:** Always double-check your calculations when working with square roots, as rounding can sometimes introduce small errors.

Learn how to find the length of the missing leg in a right triangle using the Pythagorean theorem. Step-by-step solution provided with calculations for c=8.9 and b=8.7, rounded to the nearest tenth. Suitable for Grades 7-9.

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