A 30 foot ladder is set against the side of a house so that it reaches up 24 feet. If Alexander grabs the ladder at its base and pulls it 10 feet farther from the house, how far up the side of the house will the ladder reach now? (The answer is not 14 ft.) Round to the nearest tenth of a foot.
To solve this problem, we can use the Pythagorean theorem. Let x represent the distance the ladder moves along the ground when Alexander pulls it 10 feet away from the house.
Initial ladder length = 30 ft
Initial height reached = 24 ft
Using the Pythagorean theorem:
(30 + x)^2 = 24^2 + x^2
900 + 60x + x^2 = 576 + x^2
60x = 324
x = 5.4 ft
Therefore, when the ladder is pulled 10 feet farther from the house, it will reach up approximately 19.6 feet on the side of the house.
Graph a right triangle with the two points forming the hypotenuse. Using the sides, find the distance between the two points in simplest radical form.
left bracket, minus, 9, comma, 1, right bracket, and , left bracket, minus, 3, comma, minus, 7, right bracket
(−9,1) and (−3,−7)
To find the distance between the two points (-9,1) and (-3,-7) in simplest radical form, we need to calculate the length of the hypotenuse in the right triangle formed by connecting these two points.
The distance between two points (x1, y1) and (x2, y2) is given by the distance formula:
d = √[(x2 - x1)^2 + (y2 - y1)^2]
In this case, we have:
x1 = -9, y1 = 1 (first point)
x2 = -3, y2 = -7 (second point)
So, plugging in the values:
d = √[(-3 - (-9))^2 + (-7 - 1)^2]
d = √[(-3 + 9)^2 + (-7 - 1)^2]
d = √[6^2 + (-8)^2]
d = √[36 + 64]
d = √100
d = 10
Therefore, the distance between the points (-9,1) and (-3,-7) is 10 units.