Apply the Pythagorean Theorem to find the unknown side length in the given triangle. Round your answer to the nearest tenth.
(1 point)
Responses
15.3
15.3
14.7
14.7
216
216
234
one side is 15 and the other is 3
To apply the Pythagorean Theorem, we can use the formula:
c^2 = a^2 + b^2
In this case, let's assume that 15 is one of the legs (a) and 3 is the other leg (b). The unknown side (c) will be the hypotenuse.
Substituting in the values, we have:
c^2 = 15^2 + 3^2
c^2 = 225 + 9
c^2 = 234
To find c, we need to take the square root of both sides:
c = √234
Rounding to the nearest tenth, the unknown side length is approximately 15.3.
So the correct answer is 15.3.
but what if the hypotenuse has length 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 other two sides, we need to find the length of the hypotenuse (unknown side) using the given sides.
In this case, we have two sides: one side is 15 units long and the other side is 3 units long.
To find the length of the hypotenuse, we can plug these values into the Pythagorean Theorem formula: c^2 = a^2 + b^2.
Where:
- c is the length of the hypotenuse,
- a is the length of one of the sides (15 in this case), and
- b is the length of the other side (3 in this case).
So, substituting the given values into the formula, we get: c^2 = 15^2 + 3^2.
Simplifying, we get: c^2 = 225 + 9.
Adding the right side, we have: c^2 = 234.
To find the unknown side length c, we take the square root of both sides: c = √234.
Using a calculator, we can find that √234 ≈ 15.3.
Hence, the length of the unknown side (rounded to the nearest tenth) in the given triangle is approximately 15.3 units.
If the hypotenuse has a length of 15, we can still use the Pythagorean Theorem to find the lengths of the other sides. Let's label the unknown side as x.
The formula becomes:
15^2 = a^2 + x^2
225 = a^2 + x^2
We don't have the value for a, so we can't determine x without more information.
rubbish -- we know that one leg has length 3, so
x^2 + 3^2 = 12^2
x = √135
Apologies for the confusion earlier. You are correct.
Using the Pythagorean theorem, we have:
x^2 + 3^2 = 12^2
x^2 + 9 = 144
x^2 = 144 - 9
x^2 = 135
Taking the square root of both sides:
x = √135
Rounding to the nearest tenth, the unknown side length is approximately 11.6.
So the correct answer is 11.6.