1. joshua has a ladder that is 17 ft long. he wants to lean the ladder against a vertical wall so that the top of the ladder is 16.5 ft above the ground. for safety reasons, he wants the angle the ladder makes with the ground to be no greater than 70°. will the ladder be safe at this height? show your work .

The question is asking to solve a problem that'll "add up", or in other words, makes sense; through the use of Trigonometric functions. The leaning ladder is the hypotenuse of 17ft, adjacent to that is a wall that measures 16.5ft above the ground. The angle both sides make must be <=70°. The function here is Opposite over Hypotenuse i.e 16.5/17 . We use the inverse operation of Sin which is Sin^(-1) to find if the angle is < or = to 70°. Using a calculator, we find the angle to be 76.06°, which is > more than, 70°.

Thus, the ladder will not be safe for its height and therefore won't make sense.

use an equation of ratios to determine the amount of gas needed to fill the tank.

    0.2             0.8

  =    

288.75             x

                                                              231 gal

so, 0.2x = (0.8)(288.75 gal), and x = = 1155 gal.

                                                                0.2

it would take 1155 gal. to fill the tank.

the cost would be

1155 gal         $3

* = $3465   (answer)

      1           1 gal

hope this you