The base of the 37 foot ladder is 9 feet from the wall of a building. will the top of the ladder reach a window ledge 35 feet above the ground?

-I know its a yes but what is the math in it?

You have to use the Pythagorean theorem. the formula is A squared + B squared = C squared. The formula with the numbers plugged in would look like this. 9 squared + ? = 37 squared. When we simplify it will be 81 + B squared = 1369. Now we have to subtract 81 from both sides so the equation will be 81 - 81 = B squared = 1369 - 81. 1369 - 81 is 1288. The square root of 1288 is 25 so the answer is correct.

Step-by-step explanation:

We know that
the angles opposite each other when two lines cross, they are always equal.
in this problem  ∠7 and ∠8    are vertical angles.
"vertical" refers to the vertex (where they cross), not up/down. they are also called vertically opposite angles.

let
>     ∠7
  ∠7=  ∠8

angle (5y-29) and angle 7 are supplementary angles
so
(5y-29)+  ∠7=> (5y-29)+x=> equation 1

angle (5y-29) and angle (3y+19)      are vertical angles
so
(5y-29)=(3y+> 5y-3y=19+> 2y=> y=24°

substitute the value of y in equation 1
(5y-29)+x=> (5*24-29)+x=> x=180-> x=89°

therefore

the answer is
∠7=89°
∠=89 °
y=24°