A ladder that is 15 ft long is 9 ft from the base of a wall. How far up the wall does the ladder reach

Imagine the ladder layed out flat 15 ft long. How would it be 9 ft from the base of the wall?? The ladder would have to be risen for that to make sense. So you now know that the 15 ft is the hypotenuse and that the 9 ft is the base or the distance between the base of the ladder and the base of the wall.

Use the pythagorean theorem! a^2+b^2=c^2
a^2 + 9^2 = 15^2
a^2 + 81 = 225
a^2 = 144
Then, you would get a = 12 after squaring both sides

Imagine the thing a ladder leaning on the wall. The wall is vertical. So the floor upto the base of the ladder, the wall upto the top of the ladder and the ladder itself makes a right angled triangle.

In a right angled triangle the sum of square of the base & perpeendicular = square of hypotenuse
(Pythagoras Theorem)

Hence the wall height = sqrt(15^2 - 9^2)

You can assume that the ground and the wall makes a 90 degree angle, which would make the ladder and the wall a right triangle. Since it is a right triangle, you can use the pythaagorean theorem, a^2+b^2=c^2 where c is the hypotenuse (15ft) and a and b are the sides. All you need to do is solve for b.

for 12 ft the wall reaches
the ladder reach

by using PYTHAGOREAN TRIPLET

THE REQUIRED HEIGHT=[ 15^2--9^2]^1/2

=SQRT[225--81]

=SQRT[144]

=12

15X15 = 225
9X9 = 81

225 - 81 = 144

\/144 = 12 ft ANSWER

12 ft,

What degree is it leaning? I think that is the geometry they want you to figure out.