https://file.aiquickdraw.com/mathbot/file/17272706813830fc2xmc5.jpg

The image depicts a right triangle \( \triangle ABC \) with the following dimensions:

- \( AB = 6 \, \text{m} \)
- \( BC = 4 \, \text{m} \)
- \( h \) represents the height of the triangle from vertex \( A \) to base \( BC \).

Since triangle \( ABC \) is a right triangle with \( \angle B \) being 90 degrees, we can apply the Pythagorean theorem to find the hypotenuse \( AC \).

The Pythagorean theorem states:
\[
AC^2 = AB^2 + BC^2
\]

Substituting the known values:
\[
AC^2 = 6^2 + 4^2
\]
\[
AC^2 = 36 + 16 = 52
\]
\[
AC = \sqrt{52} \approx 7.21 \, \text{m}
\]

Now, if you're looking for the height \( h \), we can use the formula for the area of a triangle, which can be expressed as:
\[
\text{Area} = \frac{1}{2} \times BC \times h
\]
Alternatively, the area can also be calculated using the sides of the triangle:
\[
\text{Area} = \frac{1}{2} \times AB \times BC
\]
Equating the two expressions for the area:
\[
\frac{1}{2} \times AB \times BC = \frac{1}{2} \times BC \times h
\]

Solving for \( h \):
\[
h = AB = 6 \, \text{m}
\]

Thus, the height \( h \) is \( 6 \, \text{m} \), which is the same as side \( AB \).

Would you like further details or have any other questions?

Here are 5 related questions:
1. How do you find the area of triangle \( ABC \)?
2. What are the properties of a right triangle?
3. How do you calculate the length of the hypotenuse in a right triangle?
4. Can the Pythagorean theorem be used in non-right triangles?
5. What is the significance of the height in triangles?

**Tip:** In any right triangle, the Pythagorean theorem is key to finding unknown sides if two sides are known.

Find the hypotenuse and height of a right triangle with sides 6 m and 4 m.

Learn how to solve a right triangle with given sides of 6 m and 4 m using the Pythagorean theorem and area formulas. Suitable for Grades 7-10 geometry students.

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