Question

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

Answer 1

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

Answer 2

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.