Math / Geometry

QuestionCeometry Pyhagorean Theorem
For the following right triangle, find the side length $x$ . Round your answer to the nearest hundredth.

Studdy Solution

STEP 1

What is this asking? We need to find the length of one side of a right triangle, knowing the lengths of the other two sides. Watch out! Don't mix up the legs and the hypotenuse in the Pythagorean theorem.
The hypotenuse is always the longest side and it's opposite the right angle!

STEP 2

1. Apply the Pythagorean Theorem
2. Solve for the Unknown Side
3. Round the Result

STEP 3

The Pythagorean theorem states that in a right triangle, the sum of the squares of the two shorter sides (legs) is equal to the square of the longest side (hypotenuse).

STEP 4

In our triangle, the legs have lengths $8$ and $x$ , and the hypotenuse has length $9$ .

STEP 5

So, we can write the equation: $8^2 + x^2 = 9^2$ .

STEP 6

Let's calculate the squares: $64 + x^2 = 81$ .

STEP 7

To isolate $x^2$ , we subtract $64$ from both sides of the equation: $x^2 = 81 - 64$ .

STEP 8

$x^2 = 17$ .

STEP 9

Now, we take the square root of both sides to find $x$ : $x = \sqrt{17}$ .

STEP 10

Since we're asked to round to the nearest hundredth, we calculate the square root: $x \approx 4.123$ .

STEP 11

Rounding $4.123$ to the nearest hundredth gives us $4.12$ .

STEP 12

The length of the unknown side, $x$ , is approximately $4.12$ .

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QuestionCeometry Pyhagorean Theorem
For the following right triangle, find the side length $x$ . Round your answer to the nearest hundredth.

Studdy Solution

STEP 1

What is this asking? We need to find the length of one side of a right triangle, knowing the lengths of the other two sides. Watch out! Don't mix up the legs and the hypotenuse in the Pythagorean theorem.
The hypotenuse is always the longest side and it's opposite the right angle!

STEP 2

1. Apply the Pythagorean Theorem
2. Solve for the Unknown Side
3. Round the Result

STEP 3

The Pythagorean theorem states that in a right triangle, the sum of the squares of the two shorter sides (legs) is equal to the square of the longest side (hypotenuse).

STEP 4

In our triangle, the legs have lengths $8$ and $x$ , and the hypotenuse has length $9$ .

STEP 5

So, we can write the equation: $8^2 + x^2 = 9^2$ .

STEP 6

Let's calculate the squares: $64 + x^2 = 81$ .

STEP 7

To isolate $x^2$ , we subtract $64$ from both sides of the equation: $x^2 = 81 - 64$ .

STEP 8

$x^2 = 17$ .

STEP 9

Now, we take the square root of both sides to find $x$ : $x = \sqrt{17}$ .

STEP 10

Since we're asked to round to the nearest hundredth, we calculate the square root: $x \approx 4.123$ .

STEP 11

Rounding $4.123$ to the nearest hundredth gives us $4.12$ .

STEP 12

The length of the unknown side, $x$ , is approximately $4.12$ .

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QuestionCeometry Pyhagorean TheoremFor the following right triangle, find the side length xxx. Round your answer to the nearest hundredth.

Studdy Solution

STEP 1

What is this asking? We need to find the length of one side of a right triangle, knowing the lengths of the other two sides. Watch out! Don't mix up the legs and the hypotenuse in the Pythagorean theorem.The hypotenuse is always the longest side and it's opposite the right angle!

STEP 2

1. Apply the Pythagorean Theorem2. Solve for the Unknown Side3. Round the Result

STEP 3

The Pythagorean theorem states that in a right triangle, the sum of the squares of the two shorter sides (legs) is equal to the square of the longest side (hypotenuse).

STEP 4

In our triangle, the legs have lengths 888 and xxx, and the hypotenuse has length 999.

STEP 5

So, we can write the equation: 82+x2=928^2 + x^2 = 9^282+x2=92.

STEP 6

Let's calculate the squares: 64+x2=8164 + x^2 = 8164+x2=81.

STEP 7

To isolate x2x^2x2, we subtract 646464 from both sides of the equation: x2=81−64x^2 = 81 - 64x2=81−64.

STEP 8

x2=17x^2 = 17x2=17.

STEP 9

Now, we take the square root of both sides to find xxx: x=17x = \sqrt{17}x=17​.

STEP 10

Since we're asked to round to the nearest hundredth, we calculate the square root: x≈4.123x \approx 4.123x≈4.123.

STEP 11

Rounding 4.1234.1234.123 to the nearest hundredth gives us **4.124.124.12**.

STEP 12

The length of the unknown side, xxx, is approximately 4.124.124.12.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionCeometry Pyhagorean Theorem
For the following right triangle, find the side length $x$ . Round your answer to the nearest hundredth.

What is this asking? We need to find the length of one side of a right triangle, knowing the lengths of the other two sides. Watch out! Don't mix up the legs and the hypotenuse in the Pythagorean theorem.
The hypotenuse is always the longest side and it's opposite the right angle!

1. Apply the Pythagorean Theorem
2. Solve for the Unknown Side
3. Round the Result

In our triangle, the legs have lengths $8$ and $x$ , and the hypotenuse has length $9$ .

So, we can write the equation: $8^2 + x^2 = 9^2$ .

Let's calculate the squares: $64 + x^2 = 81$ .

To isolate $x^2$ , we subtract $64$ from both sides of the equation: $x^2 = 81 - 64$ .

$x^2 = 17$ .

Now, we take the square root of both sides to find $x$ : $x = \sqrt{17}$ .

Since we're asked to round to the nearest hundredth, we calculate the square root: $x \approx 4.123$ .

Rounding $4.123$ to the nearest hundredth gives us $4.12$ .

The length of the unknown side, $x$ , is approximately $4.12$ .