Use the image to answer the question.
A right triangle shows the base with a value of 3, the hypotenuse on the left with a value of 15, and the perpendicular side to the base on the right with a question mark.
Apply the Pythagorean Theorem to find the unknown side length in the given triangle. Round your answer to the nearest tenth.
(1 point)
Responses
14.7
14.7
234
234
216
216
15.3
15.3
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The Pythagorean Theorem 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.
In this case, the base has a length of 3 and the hypotenuse has a length of 15. Let's call the unknown side length x.
We can set up the equation:
3^2 + x^2 = 15^2
9 + x^2 = 225
Subtract 9 from both sides:
x^2 = 216
Take the square root of both sides (since we are looking for the length of the side, not the square of its length):
x = √216
Rounding to the nearest tenth:
x ≈ 14.7
Therefore, the length of the unknown side is approximately 14.7.
To find the unknown side length in the given triangle, we can use the Pythagorean Theorem, which states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse.
The formula for the Pythagorean Theorem is as follows:
a^2 + b^2 = c^2
where "a" and "b" are the lengths of the two shorter sides (legs) of the triangle, and "c" is the length of the hypotenuse.
In this case, the base (shorter side) has a value of 3, the hypotenuse has a value of 15, and the length of the perpendicular side (unknown) is represented by "b".
Using the Pythagorean Theorem, we can set up the equation:
3^2 + b^2 = 15^2
Simplifying this equation, we have:
9 + b^2 = 225
Next, we can isolate "b^2" by subtracting 9 from both sides:
b^2 = 216
To find the value of "b", we take the square root of both sides of the equation:
√(b^2) = √216
Simplifying further, we have:
b = √216
Calculating the square root of 216, we find:
b ≈ 14.7
Therefore, rounding to the nearest tenth, the unknown side length in the triangle is approximately 14.7.
To find the length of the unknown side in a right triangle, we can apply the Pythagorean Theorem. The Pythagorean Theorem 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.
In this case, the hypotenuse is the side with a length of 15, and the base is the side with a length of 3. We need to find the length of the unknown side.
Let's denote the unknown side as x. Applying the Pythagorean Theorem, we can write the equation:
x^2 + 3^2 = 15^2
Simplifying the equation:
x^2 + 9 = 225
Next, we need to isolate x by subtracting 9 from both sides:
x^2 = 216
To find the value of x, we can take the square root of both sides. However, since we are asked to round our answer to the nearest tenth, we will only take the positive square root:
x = √(216) ≈ 14.7 (rounded to the nearest tenth)
Therefore, the length of the unknown side is approximately 14.7.