A laser pointer attached at the top of a lighthouse emits a beam that makes contact with a ship in the ocean below. The length of the laser beam is 9.8km. If the ship is 4.0km from the base of the lighthouse, determine the measure of the angle of depression, correct to the nearest degree.
I'm not sure if this is correct:
I did:
Cosx= adj/hyp
Cosx= 4.0km/9.8km
X = cos-1 = 4.0km/9.8km
X = 65.91049389
Nearest degree would be 66 degree
looks good...TALL lighthouse
Ok thanks. But you are sure it is 100% correct right? I'm sorry I'm just asking because I have a test this week and I'm stressed out..
I agree with Scott.
For the given date, the calculations are correct.
In reality, the question is absurd.
Using Pythagoras, the height of the lighthouse would have to be appr 8.9 km high.
and, using our given angle of 65.91..°
tan 65.91 = height/4
height = 4tan 65.91 = appr 8.9
Your answer is mathematically correct
To find the measure of the angle of depression, you're on the right track using the cosine function. However, the value you calculated for the inverse cosine should not be divided by 9.8km.
Let's go through the correct steps:
The adjacent side is the distance from the base of the lighthouse to the ship, which is 4.0km. The hypotenuse of the right triangle formed is the length of the laser beam, which is 9.8km.
cos(x) = adjacent / hypotenuse
cos(x) = 4.0km / 9.8km
Now, you can use the inverse cosine function to find the angle:
x = cos^(-1)(4.0km / 9.8km)
x ≈ 63.86090524 degrees
Rounding to the nearest degree, the measure of the angle of depression is approximately 64 degrees.
So, the correct answer would be 64 degrees (to the nearest degree), not 66 degrees.