Question

A ship’s guidance system measures that the ship is 380 m from the top of a lighthouse. The top of the lighthouse is 88 m above sea level. How far is the ship from the lighthouse to the nearest tenth of a meter?

Answer 1

The ship is 369.7 m away

Explanation:

Let's assign variables to the quantities given in the problem.
`d =380` m, the distance from the ship to the top of the lighthouse
`h = 88` m, the height of the lighthouse
`x = ?`, the distance from the ship to the base of the lighthouse (or the part of the lighthouse at sea level)

Using the pythagorean theorem:

`h^2 + x^2 = d^2`
`x^2 = d^2 - h^2`
`x = sqrt(d^2 - h^2)`

`x = sqrt((380 m)^2 - (88 m)^2)`
`x = 369.670123` m
`x = 369.7` m

Does this make sense?
Yes, `x` is shorter than `d` the hypotenuse of the triangle, but not by a lot. The distance of the ship to the top of the lighthouse significantly larger than the height of the lighthouse.

Answer 2

The ship is 369.7m from the lighthouse.

Explanation:

After converting the question into an image, you can see that it forms a right angle triangle, so you can use Pythagorean theorem.
`380^2-88^2=136656`
`sqrt136656=369.67`
Round to nearest tenth
`369.7`