Math / Geometry

Question1 2 4
A ladder leans against the side of a house. The top of the ladder is 20 ft from the ground. The bottom of the ladder is 15 ft from the side of the house. Find the length of the ladder. If necessary, round your answer to the nearest tenth. $\square$ ft

Studdy Solution

STEP 1

1. The ladder, the side of the house, and the ground form a right triangle.
2. The top of the ladder is 20 ft from the ground, which is one leg of the triangle.
3. The bottom of the ladder is 15 ft from the side of the house, which is the other leg of the triangle.
4. We need to find the hypotenuse of the triangle, which is the length of the ladder.

STEP 2

1. Identify the right triangle components.
2. Apply the Pythagorean Theorem.
3. Solve for the hypotenuse.
4. Round the answer to the nearest tenth if necessary.

STEP 3

Identify the components of the right triangle: - One leg is the distance from the ground to the top of the ladder: 20 ft. - The other leg is the distance from the side of the house to the bottom of the ladder: 15 ft. - The hypotenuse is the length of the ladder, which we need to find.

STEP 4

Apply 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 case: $c^2 = 20^2 + 15^2$

STEP 5

Calculate the squares of the legs: $20^2 = 400$ $15^2 = 225$

STEP 6

Add the squares of the legs to find $c^2$ : $c^2 = 400 + 225$ $c^2 = 625$

STEP 7

Solve for $c$ by taking the square root of both sides: $c = \sqrt{625}$ $c = 25$

STEP 8

Since the answer is already a whole number, no rounding is necessary.
The length of the ladder is:
$\boxed{25}$ ft

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Question1 2 4
A ladder leans against the side of a house. The top of the ladder is 20 ft from the ground. The bottom of the ladder is 15 ft from the side of the house. Find the length of the ladder. If necessary, round your answer to the nearest tenth. $\square$ ft

Studdy Solution

STEP 1

STEP 2

1. Identify the right triangle components.
2. Apply the Pythagorean Theorem.
3. Solve for the hypotenuse.
4. Round the answer to the nearest tenth if necessary.

STEP 3

Identify the components of the right triangle: - One leg is the distance from the ground to the top of the ladder: 20 ft. - The other leg is the distance from the side of the house to the bottom of the ladder: 15 ft. - The hypotenuse is the length of the ladder, which we need to find.

STEP 4

Apply 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 case: $c^2 = 20^2 + 15^2$

STEP 5

Calculate the squares of the legs: $20^2 = 400$ $15^2 = 225$

STEP 6

Add the squares of the legs to find $c^2$ : $c^2 = 400 + 225$ $c^2 = 625$

STEP 7

Solve for $c$ by taking the square root of both sides: $c = \sqrt{625}$ $c = 25$

STEP 8

Since the answer is already a whole number, no rounding is necessary.
The length of the ladder is:
$\boxed{25}$ ft

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Question1 2 4A ladder leans against the side of a house. The top of the ladder is 20 ft from the ground. The bottom of the ladder is 15 ft from the side of the house. Find the length of the ladder. If necessary, round your answer to the nearest tenth. □\square□ ft

Studdy Solution

STEP 1

STEP 2

1. Identify the right triangle components.2. Apply the Pythagorean Theorem.3. Solve for the hypotenuse.4. Round the answer to the nearest tenth if necessary.

STEP 3

Identify the components of the right triangle: - One leg is the distance from the ground to the top of the ladder: 20 ft. - The other leg is the distance from the side of the house to the bottom of the ladder: 15 ft. - The hypotenuse is the length of the ladder, which we need to find.

STEP 4

Apply the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse c c c is equal to the sum of the squares of the other two sides a a a and b b b: c2=a2+b2 c^2 = a^2 + b^2 c2=a2+b2In this case: c2=202+152 c^2 = 20^2 + 15^2 c2=202+152

STEP 5

Calculate the squares of the legs: 202=400 20^2 = 400 202=400 152=225 15^2 = 225 152=225

STEP 6

Add the squares of the legs to find c2 c^2 c2: c2=400+225 c^2 = 400 + 225 c2=400+225 c2=625 c^2 = 625 c2=625

STEP 7

Solve for c c c by taking the square root of both sides: c=625 c = \sqrt{625} c=625​ c=25 c = 25 c=25

STEP 8

Since the answer is already a whole number, no rounding is necessary. The length of the ladder is:25 \boxed{25} 25​ ft

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Studdy solves anything!

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

Question1 2 4
A ladder leans against the side of a house. The top of the ladder is 20 ft from the ground. The bottom of the ladder is 15 ft from the side of the house. Find the length of the ladder. If necessary, round your answer to the nearest tenth. $\square$ ft

1. Identify the right triangle components.
2. Apply the Pythagorean Theorem.
3. Solve for the hypotenuse.
4. Round the answer to the nearest tenth if necessary.

Apply 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 case: $c^2 = 20^2 + 15^2$

Calculate the squares of the legs: $20^2 = 400$ $15^2 = 225$

Add the squares of the legs to find $c^2$ : $c^2 = 400 + 225$ $c^2 = 625$

Solve for $c$ by taking the square root of both sides: $c = \sqrt{625}$ $c = 25$

Since the answer is already a whole number, no rounding is necessary.
The length of the ladder is:
$\boxed{25}$ ft