A 13 foot ladder is leaning against a building, with the base of the ladder 2 feet from the building. how high up on the building will the top ladder reach

Easey

makes a right triangle with the building

hypotonuse is 13

and the height and base are the legs

we know that

for a right triangle with legs lgnth a and b and hypotonuse legnth c

c²=a²+b²

c=13

a=2

b=h

13²=2²+h²

169=4+h²

minus 4

165=h²

sqrt both sides

√165=h

aprox 12.8452=h

about 12.85ft

Pythagorean Theorem,

2^2 + b^2 = 13^2, ladder is 13ft regardless of orientation so treat it has hypotenuse

b^2 = 13^2 - 4

b = sqrt (13^2 - 4)

Note, - b works as well since (-b) ^2 = b^2 but it isn't applicable in this context.