Answer:

bottom of the ladder is 24 feet from the bottom of the building.

step-by-step explanation:

use pythagorean theorem to solve for the horizontal distance along the ground between the bottoms of ladder and building.  

the pythagorean theorem states that the square of the hypotenuse (c) of the right triangle (with a 90-degree angle) is equal to the the sum of the squares of its two other sides a and b.

, c² = a² + b²

to visualize the given problem:

there are three sides that represent the sides of the right trianglethe height of the building is perpendicular to the distance along the ground creating a 90-degree angle of the right trianglethe height and distance along the ground are the two sides the ladder is the hypotenuse.

therefore:

c = 26 fta = 10 ftb =

find   b, the distance from the bottom of the ladder to the bottom of the building:

c² = a² + b²

(26 ft)² = (10 ft)² + b²

b² = (26 ft)² - (10 ft)²

b² = 676 ft² - 100 ft²

b = √(576 ft²)

b = 24 bottom of the ladder is 24 feet from the bottom of the building.

if you have an algebraic equation you can modify it to change the form of the equation and still preserve the fact that the two sides are equal. the two operations that produce such modifications are

add the same number to each side of the equation and

multiply each side of the equation by the same number.

you want to attain the form ax + by = c, that is the x and y terms on the left side of the equation and a constant on the right side. you have 3y = 4x + 1 so you need to "move" the term 4x to the left side. this you can do by adding -4x to each side.

3y = 4x + 1, so

-4x + 3y = -4x + 4x + 1, which simplifies to

-4x + 3y = 1.

this is in standard form but it seems your son's textbook wants the coefficient of x to be positive not negative. this you can achieve by multiplying each side of the equation by -1.

-4x + 3y = 1, so

-1(-4x + 3y) = -1 × 1.

multiplying -1 through the left side gives

(-1) × (-4) x + (-1) × (3) y = -1, or

4x - 3y = -1.

i hope this helps

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