Square root and property

Question

A 10-feet ladder is leaning against a building, with the base of the ladder 5 feet from the building. How high up on the building will the top of the ladder reach?

Answer 1

Pythagorean theorem

a²+ b² = c²

a and b are the two sides of the triangle (ground & building)

c is the hypotenuse (ladder)

So...

5²+ b² = 10²

25 + b² = 100

Subtract 25 from both sides (to isolate the variable)

b² = 75

Take the square root of each side

b = √75

b = √25√3

b = 5√3

The height of the building is 5√3 feet.

Answer 2

10 foot ladder 5 feet from base of wall

it's 10sin60 = 10(sqr3/2) = about 5(1.732) = about 8.66 feet high for the top of the ladder

it's 60 degree angle because 5/10=1/2 = cosine of the angle

the angle = cos^-1(1/2) = 60 degrees

or if you prefer the "square root" method

a version of the Pythagorea Theorem where hypotenuse squared = sum of squares of the other two sides

h= sqr(10^2-5^2) = sqr(100-25) = sqr75 = 5sqr3 = about 8.66 feet