Use the Pythagorean Theorem to find the missing side of the triangle. Round to the nearest tenth, if necessary.
a = ?, b = 5, c = 8
A. 6.0
B. 6.1
C. 6.2
D. 6.3
a^2 + b^2 = c^2
a^2 + b^2 = c^2
a^2 + 5^2 = 8^2
a^2 + 25 = 64
a^2 = 64 - 25
a^2 = 39
a = 6.2449 = 6.2
To use the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides, we can use the formula:
c^2 = a^2 + b^2
Given that b = 5 and c = 8, we can substitute these values into the equation:
8^2 = a^2 + 5^2
64 = a^2 + 25
Next, we can isolate the value of a^2 by subtracting 25 from both sides:
64 - 25 = a^2
39 = a^2
To find the value of a, we can take the square root of both sides:
√39 = a
This gives us approximately 6.2.
Therefore, the missing side length a is approximately 6.2.
The correct answer is C. 6.2.
To find the missing side of a triangle using the Pythagorean Theorem, we can use the formula:
a² + b² = c²
Here, a and b are the two sides of the triangle, and c is the hypotenuse. According to the given information, b = 5 and c = 8. We need to solve for the missing side a.
Substituting the given values into the formula, we get:
a² + 5² = 8²
Simplifying:
a² + 25 = 64
Subtracting 25 from both sides of the equation:
a² = 39
Now, to find the value of a, we need to take the square root of both sides of the equation:
√(a²) = √39
a = √39
Using a calculator, we can find the approximate value of √39:
a ≈ 6.24
Rounding this value to the nearest tenth, we get:
a ≈ 6.2
Therefore, the missing side of the triangle is approximately 6.2.
Hence, the correct answer is C. 6.2.