SOLUTION: 1.)A 12-foot ladder is leaning against the wall. When a painter P was 2/3 of the way of the ladder he dropped his brush which fell directly below him, 1 ft away from the wall. How

Question 254435: 1.)A 12-foot ladder is leaning against the wall. When a painter P was 2/3 of the way of the ladder he dropped his brush which fell directly below him, 1 ft away from the wall. How far was the base of the ladder on the wall?

2.)You are flying a kite and have let out 1000 feet of string. The kite string makes a 42� angle with the ground. How high is the kite?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
12 foot ladder leaning against a wall.
painter is 2/3 of the way up when he drops his brush.
brush lands directly beneath him 1 foot away from the wall.
how far from the base of the ladder is the wall.

2/3 of the way up is 8 feet on the ladder.

diagram of the ladder against the wall is shown below.

                  A

                  x
                  x x
                  x   x
                  x     x       4 feet
                  x       x
                  x         x
                  x           x
               F  x x x x x x x x  D
                  x             x x
                  x             x   x
                  x             x     x
                  x             x       x
                  x             x         x
                  x             x           x
                  x             x             x     8 feet
                  x             x               x
                  x             x                 x
                  x             x                   x
                  x             x                     x
                  x x x x x x x x x x x x x x x x x x x x 

                  C             E                       B

A is the point where the ladder touches the wall.
B is the point where the ladder touches the ground (base of the ladder).
C is the point where the wall touches the bround (base of the wall).
D is where the painter is.
E is where the brush drops
F is where a line from D parallel to the ground touches the wall.

you have formed 2 similar triangles.

they are triangle ABC and triangle ADF

the distance from C to E on the ground is 1 foot.

the distance from F to D parallel to the ground is also 1 foot.

since the triangle are similar, then their corresponding sides are proportional.

this means that AD / FD = AB / CB

since AD is 4 feet and AB is 12 feet and FD is 1 foot, this formula becomes:

4 / 1 = 12 / CB

cross multiply to get:

4*CB = 1*12

divide both sides of this equation by 4 to get:

CB = 12/4 = 3

your answer is that the distance from the base of the ladder to the base of the wall is 3 feet.

--------------------------------------------------------------------

kite is 1000 feet long from the flyer of the kite to the kite along the length of the string.

angle kite makes to the ground is 42 degrees.

this forms a triangle as shown below:


                  A

                  x
                  x x
                  x   x
                  x     x
                  x       x
                  x         x
                  x           x
                  x             x  
                  x               x   1000 feet
                  x                 x
                  x                   x
                  x                     x
                  x                       x
                  x                         x
                  x                           x
                  x                             x
                  x                               x
                  x                    42 degrees   x
                  x                                   x
                  x x x x x x x x x x x x x x x x x x x x 

                  C                                     B

point A is the kite.
point B is the person flying the kite.
point C is a point directly beneath the kite perpendicular to the ground.

the ground is represented by line segment CB

length of line segment AB is 1000 feet.

the height of the kite is represwented by line segment AC.

tangent of 42 degrees = opposite / hypotenuse = AC / AB = AC / 1000

tan(42) = AC / 1000

multiply both sides of this equation by 1000 to get:

1000 * tan(42) = AC = 900.4040443.

height of the kite is 900.4040443 feet.

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