A rope from the top of a mast on a sailboat is attached to a point 6 feet from the base of the mast. If the rope is 24 feet long, about how high is the mast?

1 Answer
Mar 27, 2018

The mast is about #"23 feet"# high.

Explanation:

Here is a diagram of the described scenario:
enter image source here

Since the mast is most likely forms a #90^@# to the ground, this is a right triangle. (This fact is demonstrated by the little square in the corner of the triangle).

So, we can use the Pythagorean Theorem to find the length of side #x#.

The Pythagorean Theorem is:
#a^2 + b^2 = c^2#
#"a = leg"#
#"b = leg"#
#"c = hypotenuse"#

We know the length of one of the legs, and the hypotenuse, so we can substitute those in and solve:

#a^2 + b^2 = c^2#

#(x)^2 + (6)^2 = (24)^2#

#x^2 + 36 = 576#

#x^2 = 540#

#x = sqrt540 #

#x ~~ "23 feet"#

So the mast is about #"23 feet"# high.