Camila needs to fix the window on the front of her house. The bottom of the window is 16 ft. from the ground. She only has a 20 ft. ladder. How far from the base of the house should she set up the ladder so that the top of the ladder is exactly at the bottom of the window?
To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let x be the distance from the base of the house to where the ladder should be set up.
Using the Pythagorean theorem, we can set up the following equation:
x^2 + 16^2 = 20^2
x^2 + 256 = 400
Subtracting 256 from both sides, we get:
x^2 = 144
Taking the square root of both sides, we get:
x = √144
x = 12 ft
Therefore, Camila should set up the ladder 12 ft from the base of the house in order for the top of the ladder to be exactly at the bottom of the window.
To determine the distance from the base of the house where Camila should set up the ladder, we can use the Pythagorean Theorem.
According to the theorem, the square of the hypotenuse (the ladder's length) is equal to the square of the other two sides.
Let x be the distance from the base of the house to the ladder's setup point.
Then, we have the following equation:
x^2 + 16^2 = 20^2
Simplifying this equation, we get:
x^2 + 256 = 400
x^2 = 400 - 256
x^2 = 144
Taking the square root of both sides, we find:
x = √144
x = 12
Therefore, Camila should set up the ladder 12 ft. from the base of the house so that the top of the ladder is exactly at the bottom of the window.
To find out how far from the base of the house Camila should set up the ladder, we can use the Pythagorean theorem. According to the theorem, in a right triangle, the square of the length of the hypotenuse (in this case, the ladder) is equal to the sum of the squares of the other two sides (the distance from the base of the house to the ladder and the distance from the ladder to the window).
Let's assume that the distance from the base of the house to the ladder is x ft. Now, we can set up the equation:
x^2 + 16^2 = 20^2
16^2 represents the height of the window, and 20^2 represents the length of the ladder. Expanding the equation:
x^2 + 256 = 400
Subtracting 256 from both sides of the equation:
x^2 = 400 - 256
x^2 = 144
To get the value of x, we can take the square root of both sides of the equation:
√(x^2) = √144
x = 12
Therefore, Camila should set up the ladder 12 ft. from the base of the house so that the top of the ladder is exactly at the bottom of the window.
Use the image to answer the question.
A rectangle is formed from two right triangles. The base of the rectangle measures 80 yards and is labeled Johnson Avenue. The top of the rectangle is labeled Edison Avenue. The left side joining both the avenues is labeled 41st street and measures 60 yards. The right side of the rectangle is labeled 42nd street. A bank is located at the vertex of 41st street and Edison Avenue. The hypotenuse joining the bank and the vertex of Johnson Avenue and 42nd street is labeled park.
Sylvia likes to walk to work when the weather is nice. She works at the bank at the corner of 41st Street and Edison Avenue. Her house is at the corner of 42nd Street and Johnson Avenue. She can walk down Johnson Avenue and turn right on 41st Street, or she can walk through the park. The distance from 42nd Street to 41st Street is 80 yards, and it is 60 yards from Johnson Avenue to Edison Avenue. Assuming the street intersections are 90° angles, how much shorter is it for Sylvia to walk through the park?
If Sylvia walks through the park instead of straight down Johnson Avenue and straight down 41st Street, the walk will be ___ yards shorter.