Apply the Pythagorean theorem to find the unknown side length in the given triangle. Round your answer to the nearest tenth. If the bottom is 3 and the long side is 15
To apply the Pythagorean theorem, which states that in a right triangle the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides, we need to label the sides of the triangle.
Let's label the bottom side as a, the unknown side as b, and the long side as c.
We are given that the bottom side, a, has a length of 3, and the long side, c, has a length of 15.
Using the Pythagorean theorem, we can write the equation as:
a^2 + b^2 = c^2
Plugging in the values we know, we have:
3^2 + b^2 = 15^2
Simplifying this equation, we get:
9 + b^2 = 225
Subtracting 9 from both sides, we have:
b^2 = 216
To find the value of b, we need to take the square root of both sides:
√(b^2) = √216
b ≈ 14.7
Rounding this to the nearest tenth, the unknown side length, b, is approximately 14.7
To find the unknown side length of the triangle using the Pythagorean theorem, we can let the unknown side be represented by the variable "x". The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the bottom side is given as 3 and the long side as 15. So, we have:
\(x^2 + 3^2 = 15^2\)
Simplifying the equation:
\(x^2 + 9 = 225\)
Subtracting 9 from both sides:
\(x^2 = 216\)
To find the value of "x", we take the square root of both sides:
\(x = \sqrt{216}\)
Calculating the square root:
\(x \approx 14.7\)
Therefore, the unknown side length is approximately 14.7 when rounded to the nearest tenth.
To apply the Pythagorean theorem to find the unknown side length, we need to consider that the theorem states:
"In a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides."
Let's assign variables to each side of the triangle to make things easier. Let's say the bottom side (base) is represented by 'a', the long side (hypotenuse) by 'c', and the unknown side (height) by 'b'.
We have the following information:
a = 3 (the bottom side)
c = 15 (the long side)
Using the Pythagorean theorem, we can write the equation as:
a² + b² = c²
Plugging in the given values, we get:
3² + b² = 15²
Simplifying this equation, we have:
9 + b² = 225
Subtracting 9 from both sides, we get:
b² = 225 - 9
b² = 216
To find 'b', we need to take the square root of both sides of the equation:
√(b²) = ±√216
Taking the square root of 216, we get:
b ≈ ±14.7
Since the side length cannot be negative in this context, we can round the answer to the nearest tenth:
b ≈ 14.7
Therefore, the unknown side length (height) of the triangle is approximately 14.7 units.