a 10-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground 9 feet from the base of the building. How high up does the ladder reach?

If this is a problem about the Pythagorean theorem, maybe this helps! If the length of the ladder is 10 feet (C) and the base is 9 feet (B), you have to multiply each number by 2, add the total of both numbers and then round the number to the nearest hundreths ( use the radical button on your calculator) and there you have it , you will have the answer on your calculator. I hope this helps ;-)

Answer Link

nobrains nobrains · Answer 2 · 2017-01-19T00:26:57+01:00

First draw a picture like the one I have (see attached).

You should know the Pythagorean theorem, which is
[tex]a^2+b^2=c^2[/tex], where a and b are the legs of the triangle and c is the hypotenuse (remember the hypotenuse is the longest side of the triangle and is opposite of the right angle).

In this case,
a = 9
b = x
c = 10

Or you could have switched up a and b and had a = x and b = 9 because they are both legs of the triangle.

Using the formula,
[tex]a^2 + b^2 = c^2 \\ (9)^2 + (x)^2 = 10^2 \\ x^2 = 10^2 - 9^2 \\ x^2 = 19 \\ x = \sqrt{19} [/tex].
Note that we elimante the negative root 19 because sides of a triangle must be positive.

The ladder reaches a height of [tex] \sqrt{19} ft [/tex], or approximately 4.359 ft.