Math / Geometry

Question3 Fill in the Blank 1 point
A 16 foot long ladder is leaning against a wall. the base of the ladder is 6 feet from the bottom of the wall. Determine how high the ladder reaches up the wall. Fill in the blank with the correct value Round to the nearest hundredth if necessary. type your answer... feet

Studdy Solution

STEP 1

1. The ladder, the wall, and the ground form a right triangle.
2. The ladder is the hypotenuse of the triangle.
3. The distance from the base of the ladder to the wall is one leg of the triangle.
4. We need to find the height the ladder reaches on the wall, which is the other leg of the triangle.

STEP 2

1. Identify the known values and the unknown value in the context of the right triangle.
2. Apply the Pythagorean Theorem to find the unknown height.
3. Solve for the height and round to the nearest hundredth if necessary.

STEP 3

Identify the known values: - The length of the ladder (hypotenuse) is $16$ feet. - The distance from the base of the ladder to the wall is $6$ feet. - The height the ladder reaches on the wall is unknown and needs to be found.

STEP 4

Apply the Pythagorean Theorem, which states $a^2 + b^2 = c^2$ , where $c$ is the hypotenuse, and $a$ and $b$ are the legs of the triangle.
In this case, let $a = 6$ feet (distance from the wall), $b$ be the height the ladder reaches on the wall, and $c = 16$ feet (length of the ladder).
$a^2 + b^2 = c^2$ $6^2 + b^2 = 16^2$

STEP 5

Calculate the squares of the known values:
$6^2 = 36$ $16^2 = 256$
Substitute these values back into the equation:
$36 + b^2 = 256$

STEP 6

Solve for $b^2$ by subtracting 36 from both sides:
$b^2 = 256 - 36$ $b^2 = 220$

STEP 7

Solve for $b$ by taking the square root of both sides:
$b = \sqrt{220}$

STEP 8

Calculate the square root of 220 and round to the nearest hundredth:
$b \approx 14.83$
The height the ladder reaches up the wall is approximately:
$\boxed{14.83} \text{ feet}$

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Studdy Solution

STEP 1

1. The ladder, the wall, and the ground form a right triangle.
2. The ladder is the hypotenuse of the triangle.
3. The distance from the base of the ladder to the wall is one leg of the triangle.
4. We need to find the height the ladder reaches on the wall, which is the other leg of the triangle.

STEP 2

1. Identify the known values and the unknown value in the context of the right triangle.
2. Apply the Pythagorean Theorem to find the unknown height.
3. Solve for the height and round to the nearest hundredth if necessary.

STEP 3

Identify the known values: - The length of the ladder (hypotenuse) is $16$ feet. - The distance from the base of the ladder to the wall is $6$ feet. - The height the ladder reaches on the wall is unknown and needs to be found.

STEP 4

STEP 5

Calculate the squares of the known values:
$6^2 = 36$ $16^2 = 256$
Substitute these values back into the equation:
$36 + b^2 = 256$

STEP 6

Solve for $b^2$ by subtracting 36 from both sides:
$b^2 = 256 - 36$ $b^2 = 220$

STEP 7

Solve for $b$ by taking the square root of both sides:
$b = \sqrt{220}$

STEP 8

Calculate the square root of 220 and round to the nearest hundredth:
$b \approx 14.83$
The height the ladder reaches up the wall is approximately:
$\boxed{14.83} \text{ feet}$

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Studdy Solution

STEP 1

1. The ladder, the wall, and the ground form a right triangle.2. The ladder is the hypotenuse of the triangle.3. The distance from the base of the ladder to the wall is one leg of the triangle.4. We need to find the height the ladder reaches on the wall, which is the other leg of the triangle.

STEP 2

1. Identify the known values and the unknown value in the context of the right triangle.2. Apply the Pythagorean Theorem to find the unknown height.3. Solve for the height and round to the nearest hundredth if necessary.

STEP 3

Identify the known values: - The length of the ladder (hypotenuse) is 16 16 16 feet. - The distance from the base of the ladder to the wall is 6 6 6 feet. - The height the ladder reaches on the wall is unknown and needs to be found.

STEP 4

STEP 5

Calculate the squares of the known values:62=36 6^2 = 36 62=36 162=256 16^2 = 256 162=256Substitute these values back into the equation:36+b2=256 36 + b^2 = 256 36+b2=256

STEP 6

Solve for b2 b^2 b2 by subtracting 36 from both sides:b2=256−36 b^2 = 256 - 36 b2=256−36 b2=220 b^2 = 220 b2=220

STEP 7

Solve for b b b by taking the square root of both sides:b=220 b = \sqrt{220} b=220​

STEP 8

Calculate the square root of 220 and round to the nearest hundredth:b≈14.83 b \approx 14.83 b≈14.83 The height the ladder reaches up the wall is approximately:14.83 feet \boxed{14.83} \text{ feet} 14.83​ feet

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Start learning now

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

1. The ladder, the wall, and the ground form a right triangle.
2. The ladder is the hypotenuse of the triangle.
3. The distance from the base of the ladder to the wall is one leg of the triangle.
4. We need to find the height the ladder reaches on the wall, which is the other leg of the triangle.

1. Identify the known values and the unknown value in the context of the right triangle.
2. Apply the Pythagorean Theorem to find the unknown height.
3. Solve for the height and round to the nearest hundredth if necessary.

Identify the known values: - The length of the ladder (hypotenuse) is $16$ feet. - The distance from the base of the ladder to the wall is $6$ feet. - The height the ladder reaches on the wall is unknown and needs to be found.

Calculate the squares of the known values:
$6^2 = 36$ $16^2 = 256$
Substitute these values back into the equation:
$36 + b^2 = 256$

Solve for $b^2$ by subtracting 36 from both sides:
$b^2 = 256 - 36$ $b^2 = 220$

Solve for $b$ by taking the square root of both sides:
$b = \sqrt{220}$

Calculate the square root of 220 and round to the nearest hundredth:
$b \approx 14.83$
The height the ladder reaches up the wall is approximately:
$\boxed{14.83} \text{ feet}$