The figure shows 2 right triangles, triangle r s t with right angle s and triangle q r t with right angle r. the measure of angle r t s is 60 degrees. the measure of angle q t r is 45 degrees. the length of side r s is 2 square root 3. the length of side q r is x. what is the value of x?

Consider right triangle RQT. In this triangle , then . Thus the triangle RQT is isosceles and RQ=RT=x.

Consider right triangle RST. In this triangle , then . The leg ST is opposite to the angle of 30°, so . 

For the right triangle RTS use the Pythagorean theorem:

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

multiplication is multiplication.   it might feel harder depending on what level of math you are in, but generally it will be the same old stuff, while implementing some new concepts and methods of solving work.