Stephanie is trying to hang holiday lights in her house. She places a 12-foot ladder against the house. The top of the ladder to reach a spot 9 feet above the ground when propped up against the house. What is the approximate distance on the ground between the base of the ladder and the house? 3 feet, 5 feet, 8 feet, 10 feet

8 ft

Step-by-step explanation:

Okay lets get our variables and notes down first, I'll use the most common terms for this.

Hypotenuse: 12 ft <-- The ladder is the hypotenuse

Leg: 9 <- The height of the top of the ladder on the house

Base: ? <- We need to solve for it.

Pythagorean Theorem says c²-a²=b²

c = Hypotenuse

a & b are both Legs and interchangeable

12²-9²=b²

144-81=b²

     63=b²

   =

   =b which is approximately 7.93 which rounds up to 8

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).