Question

a lighthouse is standing 20 meters tall and a boat is 40 meters away from the bottom of the lighthouse. determine the length from the bottom of the boat to the top of the lighthouse. round to the nearest hundredth if necessary.

Explanation:

Step1: Identify the right triangle

We have a right triangle where one leg (height of lighthouse) is \(a = 20\) meters, another leg (distance from boat to lighthouse base) is \(b = 40\) meters, and we need to find the hypotenuse \(c\) (distance from boat to lighthouse top).

Step2: Apply the Pythagorean theorem

The Pythagorean theorem states that for a right triangle, \(c=\sqrt{a^{2}+b^{2}}\). Substitute \(a = 20\) and \(b = 40\) into the formula:
\[
c=\sqrt{20^{2}+40^{2}}=\sqrt{400 + 1600}=\sqrt{2000}
\]

Step3: Simplify and round

Simplify \(\sqrt{2000}\approx44.72\) (rounded to the nearest hundredth).

Answer:

\(44.72\)