Math Problem Statement
Solution
The image depicts a right triangle with the following dimensions:
- represents the height of the triangle from vertex to base .
Since triangle is a right triangle with being 90 degrees, we can apply the Pythagorean theorem to find the hypotenuse .
The Pythagorean theorem states:
Substituting the known values:
Now, if you're looking for the height , we can use the formula for the area of a triangle, which can be expressed as: Alternatively, the area can also be calculated using the sides of the triangle: Equating the two expressions for the area:
Solving for :
Thus, the height is , which is the same as side .
Would you like further details or have any other questions?
Here are 5 related questions:
- How do you find the area of triangle ?
- What are the properties of a right triangle?
- How do you calculate the length of the hypotenuse in a right triangle?
- Can the Pythagorean theorem be used in non-right triangles?
- 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
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