Math Problem Statement

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

Solution

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

  • AB=6mAB = 6 \, \text{m}
  • BC=4mBC = 4 \, \text{m}
  • hh represents the height of the triangle from vertex AA to base BCBC.

Since triangle ABCABC is a right triangle with B\angle B being 90 degrees, we can apply the Pythagorean theorem to find the hypotenuse ACAC.

The Pythagorean theorem states: AC2=AB2+BC2AC^2 = AB^2 + BC^2

Substituting the known values: AC2=62+42AC^2 = 6^2 + 4^2 AC2=36+16=52AC^2 = 36 + 16 = 52 AC=527.21mAC = \sqrt{52} \approx 7.21 \, \text{m}

Now, if you're looking for the height hh, we can use the formula for the area of a triangle, which can be expressed as: Area=12×BC×h\text{Area} = \frac{1}{2} \times BC \times h Alternatively, the area can also be calculated using the sides of the triangle: Area=12×AB×BC\text{Area} = \frac{1}{2} \times AB \times BC Equating the two expressions for the area: 12×AB×BC=12×BC×h\frac{1}{2} \times AB \times BC = \frac{1}{2} \times BC \times h

Solving for hh: h=AB=6mh = AB = 6 \, \text{m}

Thus, the height hh is 6m6 \, \text{m}, which is the same as side ABAB.

Would you like further details or have any other questions?

Here are 5 related questions:

  1. How do you find the area of triangle ABCABC?
  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.

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Math Problem Analysis

Mathematical Concepts

Geometry
Right Triangles
Pythagorean Theorem
Area of Triangles

Formulas

Pythagorean theorem: a^2 + b^2 = c^2
Area of triangle: Area = (1/2) * base * height

Theorems

Pythagorean Theorem

Suitable Grade Level

Grades 7-10