Math / Geometry

QuestionA 10 foot ladder is placed against a building. If the base of the ladder is 7 feet away from the building, how far up the building will the ladder reach? Round the answer to the nearest tenth. $x=$ Question Help: Video

Studdy Solution

STEP 1

1. The ladder, the building, and the ground form a right triangle.
2. The ladder is the hypotenuse of the triangle.
3. We need to find the height the ladder reaches on the building, which is one of the legs of the triangle.

STEP 2

1. Identify the known values and the unknown value.
2. Use the Pythagorean theorem to set up an equation.
3. Solve for the unknown value.
4. Round the answer to the nearest tenth.

STEP 3

Identify the known values: - The length of the ladder (hypotenuse) is 10 feet. - The distance from the base of the ladder to the building is 7 feet (one leg of the triangle).
Identify the unknown value: - The height the ladder reaches on the building (the other leg of the triangle).

STEP 4

Use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse ( $c$ ) is equal to the sum of the squares of the other two sides ( $a$ and $b$ ):
$c^2 = a^2 + b^2$
In this problem: - $c = 10$ (the ladder) - $a = 7$ (the distance from the building) - $b$ is the height the ladder reaches on the building.
Set up the equation:
$10^2 = 7^2 + b^2$

STEP 5

Solve for $b$ .
First, calculate $10^2$ and $7^2$ :
$100 = 49 + b^2$
Subtract 49 from both sides to solve for $b^2$ :
$b^2 = 100 - 49$ $b^2 = 51$
Take the square root of both sides to solve for $b$ :
$b = \sqrt{51}$

STEP 6

Calculate $\sqrt{51}$ and round to the nearest tenth:
$b \approx 7.1414$
Rounded to the nearest tenth:
$b \approx 7.1$

STEP 7

The height the ladder reaches on the building is approximately:
$\boxed{7.1}$

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QuestionA 10 foot ladder is placed against a building. If the base of the ladder is 7 feet away from the building, how far up the building will the ladder reach? Round the answer to the nearest tenth. $x=$ Question Help: Video

Studdy Solution

STEP 1

1. The ladder, the building, and the ground form a right triangle.
2. The ladder is the hypotenuse of the triangle.
3. We need to find the height the ladder reaches on the building, which is one of the legs of the triangle.

STEP 2

1. Identify the known values and the unknown value.
2. Use the Pythagorean theorem to set up an equation.
3. Solve for the unknown value.
4. Round the answer to the nearest tenth.

STEP 3

Identify the known values: - The length of the ladder (hypotenuse) is 10 feet. - The distance from the base of the ladder to the building is 7 feet (one leg of the triangle).
Identify the unknown value: - The height the ladder reaches on the building (the other leg of the triangle).

STEP 4

STEP 5

Solve for $b$ .
First, calculate $10^2$ and $7^2$ :
$100 = 49 + b^2$
Subtract 49 from both sides to solve for $b^2$ :
$b^2 = 100 - 49$ $b^2 = 51$
Take the square root of both sides to solve for $b$ :
$b = \sqrt{51}$

STEP 6

Calculate $\sqrt{51}$ and round to the nearest tenth:
$b \approx 7.1414$
Rounded to the nearest tenth:
$b \approx 7.1$

STEP 7

The height the ladder reaches on the building is approximately:
$\boxed{7.1}$

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QuestionA 10 foot ladder is placed against a building. If the base of the ladder is 7 feet away from the building, how far up the building will the ladder reach? Round the answer to the nearest tenth. x=x=x= Question Help: Video

Studdy Solution

STEP 1

1. The ladder, the building, and the ground form a right triangle.2. The ladder is the hypotenuse of the triangle.3. We need to find the height the ladder reaches on the building, which is one of the legs of the triangle.

STEP 2

1. Identify the known values and the unknown value.2. Use the Pythagorean theorem to set up an equation.3. Solve for the unknown value.4. Round the answer to the nearest tenth.

STEP 3

Identify the known values: - The length of the ladder (hypotenuse) is 10 feet. - The distance from the base of the ladder to the building is 7 feet (one leg of the triangle).Identify the unknown value: - The height the ladder reaches on the building (the other leg of the triangle).

STEP 4

STEP 5

Solve for b b b.First, calculate 102 10^2 102 and 72 7^2 72:100=49+b2 100 = 49 + b^2 100=49+b2Subtract 49 from both sides to solve for b2 b^2 b2:b2=100−49 b^2 = 100 - 49 b2=100−49 b2=51 b^2 = 51 b2=51Take the square root of both sides to solve for b b b:b=51 b = \sqrt{51} b=51​

STEP 6

Calculate 51 \sqrt{51} 51​ and round to the nearest tenth:b≈7.1414 b \approx 7.1414 b≈7.1414Rounded to the nearest tenth:b≈7.1 b \approx 7.1 b≈7.1

STEP 7

The height the ladder reaches on the building is approximately:7.1 \boxed{7.1} 7.1​

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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.

QuestionA 10 foot ladder is placed against a building. If the base of the ladder is 7 feet away from the building, how far up the building will the ladder reach? Round the answer to the nearest tenth. $x=$ Question Help: Video

1. The ladder, the building, and the ground form a right triangle.
2. The ladder is the hypotenuse of the triangle.
3. We need to find the height the ladder reaches on the building, which is one of the legs of the triangle.

1. Identify the known values and the unknown value.
2. Use the Pythagorean theorem to set up an equation.
3. Solve for the unknown value.
4. Round the answer to the nearest tenth.

Identify the known values: - The length of the ladder (hypotenuse) is 10 feet. - The distance from the base of the ladder to the building is 7 feet (one leg of the triangle).
Identify the unknown value: - The height the ladder reaches on the building (the other leg of the triangle).

Solve for $b$ .
First, calculate $10^2$ and $7^2$ :
$100 = 49 + b^2$
Subtract 49 from both sides to solve for $b^2$ :
$b^2 = 100 - 49$ $b^2 = 51$
Take the square root of both sides to solve for $b$ :
$b = \sqrt{51}$

Calculate $\sqrt{51}$ and round to the nearest tenth:
$b \approx 7.1414$
Rounded to the nearest tenth:
$b \approx 7.1$

The height the ladder reaches on the building is approximately:
$\boxed{7.1}$