Math / Geometry

Question'ythagoras' theorem can be used to work out an unknown side length of a rightangled triangle.
Copy and complete the workings below to calculate the unknown side length, $a$ . $\begin{aligned} a^{2}+8^{2} & =17^{2} \\ a^{2} & =17^{2}-8^{2} \\ a^{2} & =\ldots \\ a & =\ldots . \end{aligned}$ ans
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Studdy Solution

STEP 1

1. We are given a right-angled triangle with sides $a$ , $8$ , and hypotenuse $17$ .
2. We need to find the length of the unknown side $a$ using the Pythagorean theorem.

STEP 2

1. Apply the Pythagorean theorem.
2. Simplify the equation to solve for $a^2$ .
3. Calculate the value of $a^2$ .
4. Solve for $a$ by taking the square root.

STEP 3

The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Therefore, we have:
$a^2 + 8^2 = 17^2$

STEP 4

Rearrange the equation to solve for $a^2$ :
$a^2 = 17^2 - 8^2$

STEP 5

Calculate the squares of 17 and 8:
$17^2 = 289$ $8^2 = 64$
Substitute these values back into the equation:
$a^2 = 289 - 64$

STEP 6

Perform the subtraction:
$a^2 = 289 - 64$ $a^2 = 225$

STEP 7

Solve for $a$ by taking the square root of both sides:
$a = \sqrt{225}$
Calculate the square root:
$a = 15$
The unknown side length $a$ is:
$\boxed{15}$

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Studdy Solution

STEP 1

1. We are given a right-angled triangle with sides $a$ , $8$ , and hypotenuse $17$ .
2. We need to find the length of the unknown side $a$ using the Pythagorean theorem.

STEP 2

1. Apply the Pythagorean theorem.
2. Simplify the equation to solve for $a^2$ .
3. Calculate the value of $a^2$ .
4. Solve for $a$ by taking the square root.

STEP 3

The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Therefore, we have:
$a^2 + 8^2 = 17^2$

STEP 4

Rearrange the equation to solve for $a^2$ :
$a^2 = 17^2 - 8^2$

STEP 5

Calculate the squares of 17 and 8:
$17^2 = 289$ $8^2 = 64$
Substitute these values back into the equation:
$a^2 = 289 - 64$

STEP 6

Perform the subtraction:
$a^2 = 289 - 64$ $a^2 = 225$

STEP 7

Solve for $a$ by taking the square root of both sides:
$a = \sqrt{225}$
Calculate the square root:
$a = 15$
The unknown side length $a$ is:
$\boxed{15}$

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Studdy Solution

STEP 1

1. We are given a right-angled triangle with sides a a a, 8 8 8, and hypotenuse 17 17 17.2. We need to find the length of the unknown side a a a using the Pythagorean theorem.

STEP 2

1. Apply the Pythagorean theorem.2. Simplify the equation to solve for a2 a^2 a2.3. Calculate the value of a2 a^2 a2.4. Solve for a a a by taking the square root.

STEP 3

The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Therefore, we have:a2+82=172 a^2 + 8^2 = 17^2 a2+82=172

STEP 4

Rearrange the equation to solve for a2 a^2 a2:a2=172−82 a^2 = 17^2 - 8^2 a2=172−82

STEP 5

Calculate the squares of 17 and 8:172=289 17^2 = 289 172=289 82=64 8^2 = 64 82=64Substitute these values back into the equation:a2=289−64 a^2 = 289 - 64 a2=289−64

STEP 6

Perform the subtraction:a2=289−64 a^2 = 289 - 64 a2=289−64 a2=225 a^2 = 225 a2=225

STEP 7

Solve for a a a by taking the square root of both sides:a=225 a = \sqrt{225} a=225​Calculate the square root:a=15 a = 15 a=15 The unknown side length a a a is:15 \boxed{15} 15​

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1. We are given a right-angled triangle with sides $a$ , $8$ , and hypotenuse $17$ .
2. We need to find the length of the unknown side $a$ using the Pythagorean theorem.

1. Apply the Pythagorean theorem.
2. Simplify the equation to solve for $a^2$ .
3. Calculate the value of $a^2$ .
4. Solve for $a$ by taking the square root.

The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Therefore, we have:
$a^2 + 8^2 = 17^2$

Rearrange the equation to solve for $a^2$ :
$a^2 = 17^2 - 8^2$

Calculate the squares of 17 and 8:
$17^2 = 289$ $8^2 = 64$
Substitute these values back into the equation:
$a^2 = 289 - 64$

Perform the subtraction:
$a^2 = 289 - 64$ $a^2 = 225$

Solve for $a$ by taking the square root of both sides:
$a = \sqrt{225}$
Calculate the square root:
$a = 15$
The unknown side length $a$ is:
$\boxed{15}$