Math Problem Statement
Solution
The problem shows a right triangle where one leg has a length of and the hypotenuse has a length of 6. We are tasked with finding the length of the third side, which is the other leg of the triangle.
Using the Pythagorean theorem:
The Pythagorean theorem states that for a right triangle:
Where:
- and are the lengths of the legs, and
- is the length of the hypotenuse.
Given:
- One leg ,
- Hypotenuse .
We need to find the length of the other leg, .
Step 1: Apply the Pythagorean theorem
Simplify both sides:
So the equation becomes:
Step 2: Solve for
Step 3: Solve for
Thus, the length of the third side is 3.
Would you like further details or have any questions?
Here are some related questions to explore:
- How is the Pythagorean theorem derived?
- What are the properties of right triangles?
- How do you rationalize radicals?
- Can the Pythagorean theorem be applied in 3D space?
- How do you find the area of a right triangle?
Tip: In any triangle problem, always identify whether it's a right triangle before applying the Pythagorean theorem.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Right Triangles
Pythagorean Theorem
Simplifying Radicals
Formulas
a^2 + b^2 = c^2
Square root simplification
Theorems
Pythagorean Theorem
Suitable Grade Level
Grades 8-10
Related Recommendation
Solve Right Triangle with Pythagorean Theorem: a = 3√2, c = 4√5
Find the Hypotenuse of a Right Triangle with Legs 6 and 3√13
Solve for x in a Right Triangle using the Pythagorean Theorem
Find the Hypotenuse in a Right Triangle with Legs 2 and 3
Find the Missing Side of a Right Triangle Using the Pythagorean Theorem