Apainter has a 24 foot ladder that he is using to paint a house. for safety reasons, the ladder must be placed at least 8 feet from the base of the side of the house. to the nearest tenth of a foot, how high can the ladder sanely reach?

The ladder can reach a height of 22.6 feet.  

Step-by-step explanation:

In order to find the height that the ladder can reach, you need to use the Pythagorean Theorem.  The Pythagorean Theorem assumes that the house to the ground will form a right triangle and the leaning ladder is the hypotenuse.  Using the formula:  a² + b² = c², we can plug in the values that we know and solve for the missing variable.  In this case we know the base of the triangle 'b' and the hypotenuse 'c':  a² + 8² = 24² or a² + 64 = 576.  To solve for a, we must first subtract 64 from both sides:  a² + 64 - 64 = 576 - 64 or a² = 512.  In order to find just the value of 'a', which represents the height, we need to take the square root of both sides:  √a² = √512 or a ≈ 22.6 feet.

x = 10.1

step-by-step explanation:

all of the angles of a tirangle add up to 180º

180 - 65 = 115 (since we already know the value of one angle)

(2x + 7) + (8x + 7) = 115

(combins like terms) 10x + 14 = 115

(isolate the variable subtract 14 from both sides): 10x = 101

(find the variable divide both sides by 10): x = 101/10

x = 10.1

step-by-step explanation: