Math Problem Statement
Solution
The image shows a right triangle with two known sides: 40 and 9, and the unknown side labeled , which we need to find.
We can use the Pythagorean Theorem to solve for , which is typically used for right triangles. The Pythagorean theorem states:
Where:
- and are the legs of the triangle,
- is the hypotenuse (the longest side, opposite the right angle).
From the image:
- One leg ,
- The other leg ,
- The hypotenuse .
Substitute into the Pythagorean theorem:
Now, take the square root of both sides to solve for :
So, the side length is approximately 38.98 units.
Would you like further clarification on any part of the solution? Here are five related questions you might find helpful:
- What conditions are necessary to apply the Pythagorean Theorem?
- Can the Pythagorean Theorem be used in non-right triangles?
- How can you check if a triangle is a right triangle given its sides?
- What other methods are there to find missing sides of triangles besides the Pythagorean Theorem?
- How can you find the angles in a right triangle if you know all the sides?
Tip: When applying the Pythagorean theorem, always make sure the hypotenuse is correctly identified as the longest side.
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Math Problem Analysis
Mathematical Concepts
Geometry
Right Triangles
Algebra
Formulas
Pythagorean theorem: a^2 + b^2 = c^2
Theorems
Pythagorean Theorem
Suitable Grade Level
Grades 8-10
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