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
234
234
216
216
15.3
15.3
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 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.
In this case, the base has a value of 3 and the hypotenuse has a value of 15.
Using the Pythagorean Theorem, we can set up the equation:
3^2 + x^2 = 15^2
Simplifying:
9 + x^2 = 225
Subtracting 9 from both sides:
x^2 = 225 - 9
x^2 = 216
Taking the square root of both sides:
x ≈ √216
x ≈ 14.7 (rounded to the nearest tenth)
Therefore, the unknown side length is approximately 14.7.
To find the unknown side length in the right triangle using the Pythagorean Theorem, we can use the formula:
a² + b² = c²
where:
a = length of the base = 3
c = length of the hypotenuse = 15
b = unknown side length
Now, we can substitute the known values into the formula:
3² + b² = 15²
9 + b² = 225
Next, we can isolate the variable:
b² = 225 - 9
b² = 216
Finally, we can find the value of b by taking the square root of both sides:
b = √216
b ≈ 14.7
Therefore, the unknown side length is approximately 14.7, so the correct answer is 14.7.
if a triangle
To find the length of the unknown side in the given right triangle, we can apply the Pythagorean Theorem. The Pythagorean Theorem 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.
In this case, the base has a length of 3 and the hypotenuse has a length of 15. Let's denote the length of the unknown side as x.
Using the Pythagorean Theorem, we can set up the equation:
3^2 + x^2 = 15^2
Simplifying this equation, we have:
9 + x^2 = 225
Next, we can isolate x^2 by subtracting 9 from both sides:
x^2 = 225 - 9
x^2 = 216
Taking the square root of both sides, we find:
x ≈ √216
x ≈ 14.7
Therefore, the length of the unknown side, rounded to the nearest tenth, is approximately 14.7.