Math Problem Statement
Solution
To find the value of in the right triangle shown, we can use the Pythagorean theorem:
where is the hypotenuse, and and are the two legs of the right triangle.
Here:
- (the unknown side we need to solve for)
- (the hypotenuse)
Applying the Pythagorean theorem:
Calculating each term:
Now substitute these values:
Subtract 81 from both sides:
Take the square root of both sides:
So, the correct answer is:
(B)
Would you like further details on this solution, or have any additional questions?
Here are 5 related questions that can help deepen your understanding:
- How can the Pythagorean theorem be applied to other types of triangles?
- What happens if all sides of a triangle are known? Can we still use the Pythagorean theorem?
- How does one determine if a triangle is a right triangle using only side lengths?
- If one side of a right triangle is doubled, how does that affect the hypotenuse?
- Can the Pythagorean theorem be used in three-dimensional space?
Tip: Always verify which side is the hypotenuse in a right triangle when applying the Pythagorean theorem.
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Math Problem Analysis
Mathematical Concepts
Geometry
Right Triangle
Pythagorean Theorem
Formulas
a^2 + b^2 = c^2
Theorems
Pythagorean Theorem
Suitable Grade Level
Grade 8-10
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