A ladder is leaning against a house at an angle of 39°. If the latter is 12 feet long, how far is the bottom of the ladder from the house?

9.32 ft

Step-by-step explanation:

Hi, since the situation forms a right triangle (see attachment) we have to apply the next trigonometric function.  

Cos α = adjacent side / hypotenuse  

Where α is the angle of elevation of the ladder to the ground, the hypotenuse is the longest side of the triangle (in this case is the length of the ladder), and the adjacent side (x) is the distance between the bottom of the ladder and the house.

Replacing with the values given:  

cos 39 = x/ 12

Solving for x  

cos39 (12) =x  

x= 9.32 ft

Feel free to ask for more if needed or if you did not understand something.  

x > 1.3

step by step:

8.5−0.9x> 9.8−1.9x

step 1: simplify both sides of the inequality.

−0.9x+8.5> −1.9x+9.8

step 2: add 1.9x to both sides.

−0.9x+8.5+1.9x> −1.9x+9.8+1.9x

1x+8.5> 9.8

step 3: subtract 8.5 from both sides.

1x+8.5−8.5> 9.8−8.5

1x> 1.3

step 4: divide both sides by 1.

1x/1 > 1.3/1