A 12 foot ladder is leaning against a brick wall. The top of the ladder touches the wall 6 ft above the ground. What is the angle form from the base of the ladder to the ground
To find the angle formed between the base of the ladder and the ground, we can use trigonometry. In this case, we have a right triangle formed by the ladder, the wall, and the ground.
Let's label the sides of the triangle:
- The height of the wall where the ladder touches it is 6 feet.
- The length of the ladder is 12 feet.
- The distance from the base of the ladder to the wall is the hypotenuse of the triangle.
Using the Pythagorean theorem, we can find the length of the base of the triangle:
(base)^2 + (height)^2 = (hypotenuse)^2
Let's calculate it:
(base)^2 + (6 ft)^2 = (12 ft)^2
(base)^2 + 36 ft^2 = 144 ft^2
(base)^2 = 144 ft^2 - 36 ft^2
(base)^2 = 108 ft^2
base = sqrt(108 ft^2)
base ≈ 10.39 ft
Now, we can find the angle by using the trigonometric function tangent (tan):
tan(angle) = (height)/(base)
tan(angle) = 6 ft / 10.39 ft
To find the angle, we need to take the inverse tangent (arctan) of both sides:
angle = arctan(6 ft / 10.39 ft)
Using a calculator, we can find that the angle is approximately 29.56 degrees.
Therefore, the angle formed from the base of the ladder to the ground is approximately 29.56 degrees.
To find the angle formed between the base of the ladder and the ground, we can use trigonometry. In this case, we have a right triangle formed by the ladder, the wall, and the ground.
Let's label the sides of the triangle:
- The height of the wall where the ladder touches it is 6 feet.
- The length of the ladder is 12 feet.
- The distance from the base of the ladder to the wall is the hypotenuse of the triangle.
Using the Pythagorean theorem, we can find the length of the base of the triangle:
(base)^2 + (height)^2 = (hypotenuse)^2
Let's calculate it:
(base)^2 + (6 ft)^2 = (12 ft)^2
(base)^2 + 36 ft^2 = 144 ft^2
(base)^2 = 144 ft^2 - 36 ft^2
(base)^2 = 108 ft^2
base = sqrt(108 ft^2)
base ≈ 10.39 ft
Now, we can find the angle by using the trigonometric function tangent (tan):
tan(angle) = (height)/(base)
tan(angle) = 6 ft / 10.39 ft
To find the angle, we need to take the inverse tangent (arctan) of both sides:
angle = arctan(6 ft / 10.39 ft)
Using a calculator, we can find that the angle is approximately 29.56 degrees.
Therefore, the angle formed from the base of the ladder to the ground is approximately 29.56 degrees.
Answers & Comments
Answer:
To find the angle formed between the base of the ladder and the ground, we can use trigonometry. In this case, we have a right triangle formed by the ladder, the wall, and the ground.
Let's label the sides of the triangle:
- The height of the wall where the ladder touches it is 6 feet.
- The length of the ladder is 12 feet.
- The distance from the base of the ladder to the wall is the hypotenuse of the triangle.
Using the Pythagorean theorem, we can find the length of the base of the triangle:
(base)^2 + (height)^2 = (hypotenuse)^2
Let's calculate it:
(base)^2 + (6 ft)^2 = (12 ft)^2
(base)^2 + 36 ft^2 = 144 ft^2
(base)^2 = 144 ft^2 - 36 ft^2
(base)^2 = 108 ft^2
base = sqrt(108 ft^2)
base ≈ 10.39 ft
Now, we can find the angle by using the trigonometric function tangent (tan):
tan(angle) = (height)/(base)
tan(angle) = 6 ft / 10.39 ft
To find the angle, we need to take the inverse tangent (arctan) of both sides:
angle = arctan(6 ft / 10.39 ft)
Using a calculator, we can find that the angle is approximately 29.56 degrees.
Therefore, the angle formed from the base of the ladder to the ground is approximately 29.56 degrees.
Step-by-step explanation:
Verified answer
Answer:
To find the angle formed between the base of the ladder and the ground, we can use trigonometry. In this case, we have a right triangle formed by the ladder, the wall, and the ground.
Let's label the sides of the triangle:
- The height of the wall where the ladder touches it is 6 feet.
- The length of the ladder is 12 feet.
- The distance from the base of the ladder to the wall is the hypotenuse of the triangle.
Using the Pythagorean theorem, we can find the length of the base of the triangle:
(base)^2 + (height)^2 = (hypotenuse)^2
Let's calculate it:
(base)^2 + (6 ft)^2 = (12 ft)^2
(base)^2 + 36 ft^2 = 144 ft^2
(base)^2 = 144 ft^2 - 36 ft^2
(base)^2 = 108 ft^2
base = sqrt(108 ft^2)
base ≈ 10.39 ft
Now, we can find the angle by using the trigonometric function tangent (tan):
tan(angle) = (height)/(base)
tan(angle) = 6 ft / 10.39 ft
To find the angle, we need to take the inverse tangent (arctan) of both sides:
angle = arctan(6 ft / 10.39 ft)
Using a calculator, we can find that the angle is approximately 29.56 degrees.
Therefore, the angle formed from the base of the ladder to the ground is approximately 29.56 degrees.
Step-by-step explanation: