Math / Geometry

QuestionFor the following right triangle, find the side length $x$ .

Studdy Solution

STEP 1

1. The triangle is a right triangle.
2. The Pythagorean Theorem applies, 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.

STEP 2

1. Identify the sides of the triangle.
2. Apply the Pythagorean Theorem.
3. Solve for $x$ .

STEP 3

Identify the sides of the triangle. In this problem, the sides are given as 8 and 15, and the hypotenuse is labeled $x$ .

STEP 4

Apply the Pythagorean Theorem, which is given by:
$a^2 + b^2 = c^2$
where $a$ and $b$ are the legs of the triangle, and $c$ is the hypotenuse.
For this problem, we have:
$8^2 + 15^2 = x^2$

STEP 5

Calculate the squares of the given side lengths:
$8^2 = 64$ $15^2 = 225$

STEP 6

Sum the squares of the side lengths:
$64 + 225 = 289$

STEP 7

Solve for $x$ by taking the square root of both sides of the equation:
$x^2 = 289$ $x = \sqrt{289}$

STEP 8

Evaluate the square root:
$x = \sqrt{289} = 17$
The side length $x$ is:
$\boxed{17}$

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QuestionFor the following right triangle, find the side length $x$ .

Studdy Solution

STEP 1

1. The triangle is a right triangle.
2. The Pythagorean Theorem applies, 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.

STEP 2

1. Identify the sides of the triangle.
2. Apply the Pythagorean Theorem.
3. Solve for $x$ .

STEP 3

Identify the sides of the triangle. In this problem, the sides are given as 8 and 15, and the hypotenuse is labeled $x$ .

STEP 4

Apply the Pythagorean Theorem, which is given by:
$a^2 + b^2 = c^2$
where $a$ and $b$ are the legs of the triangle, and $c$ is the hypotenuse.
For this problem, we have:
$8^2 + 15^2 = x^2$

STEP 5

Calculate the squares of the given side lengths:
$8^2 = 64$ $15^2 = 225$

STEP 6

Sum the squares of the side lengths:
$64 + 225 = 289$

STEP 7

Solve for $x$ by taking the square root of both sides of the equation:
$x^2 = 289$ $x = \sqrt{289}$

STEP 8

Evaluate the square root:
$x = \sqrt{289} = 17$
The side length $x$ is:
$\boxed{17}$

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QuestionFor the following right triangle, find the side length xxx.

Studdy Solution

STEP 1

1. The triangle is a right triangle.2. The Pythagorean Theorem applies, 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.

STEP 2

1. Identify the sides of the triangle.2. Apply the Pythagorean Theorem.3. Solve for x x x.

STEP 3

Identify the sides of the triangle. In this problem, the sides are given as 8 and 15, and the hypotenuse is labeled x x x.

STEP 4

Apply the Pythagorean Theorem, which is given by:a2+b2=c2 a^2 + b^2 = c^2 a2+b2=c2where a a a and b b b are the legs of the triangle, and c c c is the hypotenuse.For this problem, we have:82+152=x2 8^2 + 15^2 = x^2 82+152=x2

STEP 5

Calculate the squares of the given side lengths:82=64 8^2 = 64 82=64 152=225 15^2 = 225 152=225

STEP 6

Sum the squares of the side lengths:64+225=289 64 + 225 = 289 64+225=289

STEP 7

Solve for x x x by taking the square root of both sides of the equation:x2=289 x^2 = 289 x2=289 x=289 x = \sqrt{289} x=289​

STEP 8

Evaluate the square root:x=289=17 x = \sqrt{289} = 17 x=289​=17 The side length x x x is:17 \boxed{17} 17​

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QuestionFor the following right triangle, find the side length $x$ .

1. The triangle is a right triangle.
2. The Pythagorean Theorem applies, 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.

1. Identify the sides of the triangle.
2. Apply the Pythagorean Theorem.
3. Solve for $x$ .

Identify the sides of the triangle. In this problem, the sides are given as 8 and 15, and the hypotenuse is labeled $x$ .

Apply the Pythagorean Theorem, which is given by:
$a^2 + b^2 = c^2$
where $a$ and $b$ are the legs of the triangle, and $c$ is the hypotenuse.
For this problem, we have:
$8^2 + 15^2 = x^2$

Calculate the squares of the given side lengths:
$8^2 = 64$ $15^2 = 225$

Sum the squares of the side lengths:
$64 + 225 = 289$

Solve for $x$ by taking the square root of both sides of the equation:
$x^2 = 289$ $x = \sqrt{289}$

Evaluate the square root:
$x = \sqrt{289} = 17$
The side length $x$ is:
$\boxed{17}$