Question

A rope from the top of a mast on a sailboat is attached to a point 19 feet from the mast. If the rope

is 28 feet long, how tall is the mast? Round to the nearest tenth of a foot.

Answer 1

Let h represent height of mast.

We have been given that a from the top of a mast on a sailboat is attached to a point 19 feet from the mast. The rope  is 28 feet long. We are asked to find the height of the mast.

The mast will form a right triangle with rope and sailboat as shown in the attachment.

Now we will use Pythagoras theorem to solve for h as:

$h^2=28^2-19^2$

$h^2=784-361$

$h^2=423$

Now we will take positive square root of both sides as:

$\sqrt{h^2}=\sqrt{423}$

$h=20.56696380$

Upon rounding to nearest tenth of a foot, we will get:

$h\approx 20.6$

Therefore, the mast is approximately 20.6 feet tall.

Answer 2

The height of the mast is 20.6 feet.

Given information:

A rope from the top of a mast on a sailboat is attached to a point 19 feet from the mast. Let this distance be x.

The length of the rope is 28 feet. Let this length be l.

It is required to calculate the height of the mast (h).

Now, the three lengths l, h, and x will form a right angled triangle. So, Pythagoras theorem can be applied here.

So, the height h of the mast can be calculated as,

$l^2=h^2+x^2\\28^2=h^2+19^2\\h^2=423\\h=20.56\\h=20.6\rm\;ft$

Therefore, the height of the mast is 20.6 feet.

For more details about Pythagoras theorem, refer to the link:

https://brainly.com/question/343682