A 25 ft ladder is leaning against a tree. The bottom of the ladder is 7 feet away from the bottom of the tree. How high up the tree does the top of the ladder reach

the height of the tree to the top of the ladder is 24ft

Step-by-step explanation:

To solve this we need to know the Pythagorean theorem that is used for triangles with a right angle

h = hypotenuse

c1 = leg one

c2 = leg two

h ^2 = l1^2 + l2^2

the 25ft of the stairs represent the hypotenuse and the 7ft one of the 2 legs

then we just have to clear the missing leg and solve

h ^2 = l1^2 + l2^2

c2^2 = h ^2 - c1^2

c2 = √ (h ^2 - c1^2)

c2 = √ (25^2 - 7^2)

c2 = √ (625 - 49)

c2 = √576

c2 = 24ft

then the height of the tree to the top of the ladder is 24ft