A 14 foot ladder is leaning against a building. The ladder makes a 45 degree angle with the building. How far up the building does the ladder reach.

feet

Step-by-step explanation:

This question uses special right triangles.

There are two main special triangles to remember.

Attached is a diagram of the triangle. Both the base and the height are the same, so the 14 foot-long ladder is the hypotenuse.

The hypotenuse of a 45-45-90 triangle is equal to , where k is the side length.

We can solve for the side lengths by using this equation:

Simplifying this equation by dividing both sides by the square root of 2 and rationalizing the denominator, we get

Your side length of the height of the triangle is equal to 7 times the square root of 2.

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional