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?(1 point) ft.
To solve this problem, we can use the Pythagorean theorem.
Let's assume that the distance from the base of the house to where Camila sets up the ladder is x feet.
According to the Pythagorean theorem:
x^2 + 16^2 = 20^2
x^2 + 256 = 400
x^2 = 400 - 256
x^2 = 144
Taking the square root of both sides:
x = 12
Therefore, Camila should set up the ladder 12 feet from the base of the house.
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?(1 point)If Sylvia walks through the park instead of straight down Johnson Avenue and straight down 41st Street, the walk will be yards shorter.
If Sylvia walks down Johnson Avenue and then turns right on 41st Street, she will be walking a distance of 80 yards + 60 yards = <<80+60=140>>140 yards.
If Sylvia walks through the park, she will be walking a diagonal distance. Using the Pythagorean theorem, the diagonal distance can be calculated as follows:
Diagonal distance = √(80^2 + 60^2) = √(6400 + 3600) = √10000 = 100 yards
Therefore, if Sylvia walks through the park instead of straight down Johnson Avenue and straight down 41st Street, the walk will be 140 – 100 = <<140-100=40>>40 yards shorter.
To find the distance from the base of the house where Camila should set up the ladder, we can use the Pythagorean theorem.
Let's assume that the distance from the base of the house to the ladder is x ft. We can then set up the following equation:
x^2 + 16^2 = 20^2
Simplifying the equation:
x^2 + 256 = 400
Subtracting 256 from both sides:
x^2 = 400 - 256
x^2 = 144
Taking the square root of both sides:
x = sqrt(144)
x = 12 ft.
Therefore, Camila should set up the ladder 12 ft. from the base of the house.