A rectangular window is 4x inches wide and 8x inches long. What is an expression for the distance from one corner of the window to the opposite corner? Give your answer as a simplified radical.

Step-by-step explanation:

Pythagorean theorem

a² + b² = c²          a = 4x     b=8x

c = √(a² + b²)

c =√((4x)² + (8x)²)

  = √(16x² + 64x²)

  = √80x²

  = √(16×5)x²

  = 4x√5

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).