A painter leans a 15 ft ladder against a house. The base of the ladder is 5 ft from the house. a) To the nearest tenth of a foot, how high on the house does the ladder reach? b) The ladder in part (a) reaches too high on the house. By how much should the painter move the ladder's base away from the house to lower the top by 1 ft?

oops

I checked my math again and that final answer should have been 7.23 ft, not 14.555

You must be studying the Pythagorean Theorem.

Did you make a diagram?
make the ladder the hypotenuse of 15, the height as h, and the base as 5

then solve h^2 + 5^2 = 15^2

b) take the answer from a), reduce the height by 1 and do a new equation.

(I got a base of 14.555 for b) )

8-foot ladder leaning a wall and make 53 degree angle

To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.

Let's solve part (a) first:

Given:
Base of the ladder (one side of the right triangle) = 5 ft
Length of the ladder (the hypotenuse of the right triangle) = 15 ft

Let the height on the house (the other side of the right triangle) be x ft.

Using the Pythagorean theorem, we can set up the equation:
(5)^2 + (x)^2 = (15)^2

Simplifying the equation:
25 + x^2 = 225

Rearranging the equation:
x^2 = 225 - 25
x^2 = 200

Taking the square root of both sides:
x = √200

Calculating the value to the nearest tenth:
x ≈ 14.1 ft

Therefore, the ladder reaches approximately 14.1 ft high on the house.

Now, let's solve part (b):

The painter needs to lower the top of the ladder by 1 ft. This means that the height on the house should be reduced from 14.1 ft to 14.1 ft - 1 ft = 13.1 ft.

Again, let's use the Pythagorean theorem to find the new distance from the base of the ladder to the house.

Let the new distance be y ft.

Using the Pythagorean theorem, we can set up the equation:
(5 + y)^2 + (13.1)^2 = (15)^2

Simplifying the equation:
25 + 10y + y^2 + 171.61 = 225

Rearranging the equation:
y^2 + 10y + 146.39 = 0

This is a quadratic equation, and we can solve it using the quadratic formula:
y = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 1, b = 10, and c = 146.39.

Calculating the values:
y = (-10 ± √(10^2 - 4*1*146.39)) / (2*1)
y = (-10 ± √(100 - 585.56)) / 2
y = (-10 ± √(-485.56)) / 2

The value inside the square root is negative, so there are no real solutions for y in this case. This means that the ladder cannot be moved to lower the top by exactly 1 ft.

However, if you still want to find an approximate solution, you can use the quadratic formula and approximate the square root of a negative number using complex numbers. In this specific context, it may not be practical or meaningful to do so.

Therefore, in part (b), the ladder cannot be moved to lower the top by exactly 1 ft.

pretty sure the answer is MILK