QuestionFind the length of the ladder needed if it reaches 16 feet high and is placed 12 feet from the wall. Use $a^2 + b^2 = c^2$ .

Studdy Solution

STEP 1

Assumptions1. The height of the shingle from the ground is16 feet. . The foot of the ladder is placed12 feet away from the wall.
3. The ladder, the wall, and the ground form a right triangle.
4. We need to find the length of the ladder, which is the hypotenuse of the right triangle.

STEP 2

We can use the Pythagorean theorem to solve this problem. The theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). This can be written as $c^2 = a^2 + b^2$

STEP 3

In this problem, the height of the shingle from the ground is one side of the triangle (a), and the distance of the foot of the ladder from the wall is the other side (b). We are trying to find the length of the ladder, which is the hypotenuse (c). So we can plug in the given values into the Pythagorean theorem $c^2 = (16\, feet)^2 + (12\, feet)^2$

STEP 4

Calculate the squares of the lengths of the sides.
$c^2 =256\, feet^2 +144\, feet^2$

STEP 5

Add the squares of the lengths of the sides.
$c^2 =400\, feet^2$

STEP 6

Now, to find the length of the ladder (c), we need to take the square root of both sides of the equation.
$c = \sqrt{400\, feet^2}$

STEP 7

Calculate the length of the ladder.
$c =20\, feet$ Claire's mom needs a ladder that is20 feet long.

Was this helpful?

QuestionFind the length of the ladder needed if it reaches 16 feet high and is placed 12 feet from the wall. Use $a^2 + b^2 = c^2$ .

Studdy Solution

STEP 1

Assumptions1. The height of the shingle from the ground is16 feet. . The foot of the ladder is placed12 feet away from the wall.
3. The ladder, the wall, and the ground form a right triangle.
4. We need to find the length of the ladder, which is the hypotenuse of the right triangle.

STEP 2

We can use the Pythagorean theorem to solve this problem. The theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). This can be written as $c^2 = a^2 + b^2$

STEP 3

STEP 4

Calculate the squares of the lengths of the sides.
$c^2 =256\, feet^2 +144\, feet^2$

STEP 5

Add the squares of the lengths of the sides.
$c^2 =400\, feet^2$

STEP 6

Now, to find the length of the ladder (c), we need to take the square root of both sides of the equation.
$c = \sqrt{400\, feet^2}$

STEP 7

Calculate the length of the ladder.
$c =20\, feet$ Claire's mom needs a ladder that is20 feet long.

Get Studdy

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.

QuestionFind the length of the ladder needed if it reaches 16 feet high and is placed 12 feet from the wall. Use a2+b2=c2a^2 + b^2 = c^2a2+b2=c2.

Studdy Solution

STEP 1

Assumptions1. The height of the shingle from the ground is16 feet. . The foot of the ladder is placed12 feet away from the wall.3. The ladder, the wall, and the ground form a right triangle.4. We need to find the length of the ladder, which is the hypotenuse of the right triangle.

STEP 2

We can use the Pythagorean theorem to solve this problem. The theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). This can be written asc2=a2+b2c^2 = a^2 + b^2c2=a2+b2

STEP 3

STEP 4

Calculate the squares of the lengths of the sides.c2=256 feet2+144 feet2c^2 =256\, feet^2 +144\, feet^2c2=256feet2+144feet2

STEP 5

Add the squares of the lengths of the sides.c2=400 feet2c^2 =400\, feet^2c2=400feet2

STEP 6

Now, to find the length of the ladder (c), we need to take the square root of both sides of the equation.c=400 feet2c = \sqrt{400\, feet^2}c=400feet2​

STEP 7

Calculate the length of the ladder.c=20 feetc =20\, feetc=20feetClaire's mom needs a ladder that is20 feet long.

Get Studdy

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.

QuestionFind the length of the ladder needed if it reaches 16 feet high and is placed 12 feet from the wall. Use $a^2 + b^2 = c^2$ .

Assumptions1. The height of the shingle from the ground is16 feet. . The foot of the ladder is placed12 feet away from the wall.
3. The ladder, the wall, and the ground form a right triangle.
4. We need to find the length of the ladder, which is the hypotenuse of the right triangle.

We can use the Pythagorean theorem to solve this problem. The theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). This can be written as $c^2 = a^2 + b^2$

Calculate the squares of the lengths of the sides.
$c^2 =256\, feet^2 +144\, feet^2$

Add the squares of the lengths of the sides.
$c^2 =400\, feet^2$

Now, to find the length of the ladder (c), we need to take the square root of both sides of the equation.
$c = \sqrt{400\, feet^2}$

Calculate the length of the ladder.
$c =20\, feet$ Claire's mom needs a ladder that is20 feet long.