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?

2 Answers
Feb 16, 2018

The ship is 369.7 m away

Explanation:

diagram of the problemdiagram of the problem

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.

Feb 16, 2018

The ship is 369.7m from the lighthouse.

Explanation:

enter image source here
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