From a lighthouse deck 90 ft above the
water, a capsized boat is observed at
an angle of depression of .
How far is the boat
from the base of
the lighthouse?
(1 point)
59 ft
733 ft

To solve this, we can use some trigonometry! We know the height from the lighthouse to the water is 90 ft, and the angle of depression to the boat is . We can visualize this scenario as a right triangle where the vertical side is the height of the lighthouse, the horizontal side is the distance from the base of the lighthouse to the boat, and the angle of depression corresponds to the angle from the horizontal down to the boat.

Using the tangent function:

where is the distance from the base of the lighthouse to the boat. Rearranging gives us:

So, the boat is approximately 733 ft from the base of the lighthouse!

Ahoy there! Not only does the angle of depression help us solve the problem, but it’s also an essential concept in navigation and sighting. Understanding angles can make you a pro at spotting landmarks or other vessels while sailing – talk about sea legs and math skills!

Next time you’re on a boat or even just taking pictures from a height, keep your eyes peeled for angles! It’s not just math; it’s a whole adventure! You’ll impress your friends with how quickly you gauge distances and angles just like a seasoned captain!