An historic lighthouse is 200 yards from a bike path along the edge of a lake. A walk to the lighthouse is 400 yards long. Find the acute angle feta between the bike path and the walkway.
I found sin which was 1/2. The book says feta is 30 degrees. But how does the value of sin contribute to this and where does thirty degrees come from?
You are correct to say that sin(theta) = 1/2
we also know that sin 30 = 1/2
so isn't theta = 30 ?
Make sure your calculator is set to degrees.
enter
200 / 400
=
press 2ndF or INV, whichever your calculator uses
press SIN
=
you should get 30 degrees.
BTW, who is this feta guy? Did you mean theta, the Greek letter?
I think feta is some kind of cheese.
Ah, the mysterious feta angle! Are we talking about a cheese or a Greek letter here? Either way, let's have some fun with this one.
It seems like you've got the sine of the feta angle figured out, with a value of 1/2. That means the ratio of the opposite side to the hypotenuse is 1/2. But where does the 30 degrees come from?
Well, lucky for us, the sine of 30 degrees (or π/6 radians) is indeed 1/2! So, it looks like feta angle is 30 degrees or π/6 radians.
And remember, in the world of geometry, angles and ratios like to party together and do some funky dance moves. So, the sine value leads us to the angle, and the angle gives us the sine. It's all connected, just like a good joke setup and punchline!
Now go have some cheese or Greek lessons, whichever you prefer!
To find the angle feta between the bike path and the walkway, we can use the trigonometric relationship between the sides of a right triangle.
Let's assume that the bike path and walkway form the two legs of a right triangle. The distance from the bike path to the lighthouse is the opposite side, and the length of the walkway is the hypotenuse.
In this case, we know that the length of the walkway is 400 yards, and the distance from the bike path to the lighthouse is 200 yards.
To find the acute angle feta, we can use the sine function, which is defined as the ratio of the length of the opposite side to the length of the hypotenuse in a right triangle. In this case, we have:
sin(feta) = opposite/hypotenuse
Substituting the known values:
sin(feta) = 200/400
simplifying:
sin(feta) = 1/2
Now, we need to find the angle feta whose sine is 1/2. To do this, we can use the inverse sine function (also called arcsine or sin^(-1)).
feta = inverse sine(1/2)
Using a calculator, we find:
feta ≈ 30 degrees
So, the acute angle between the bike path and the walkway is approximately 30 degrees. The value of the sine function, in this case, tells us the ratio between the opposite side and the hypotenuse, which helps us determine the angle.
To find the acute angle feta between the bike path and the walkway, you can use trigonometric ratios. In this case, the ratio that is useful is the sine function.
Let's start by drawing a diagram of the situation. You have a bike path along the edge of a lake, and the lighthouse is 200 yards away from the path. The walk to the lighthouse is 400 yards long.
If we let theta be the acute angle between the bike path and the walkway, the adjacent side is the distance from the lighthouse to the path, which is 200 yards, and the hypotenuse is the walkway, which is 400 yards.
Now, let's use the definition of the sine function: sin(theta) = opposite/hypotenuse.
In this case, the opposite side is the distance from the lighthouse to the path, which is 200 yards, and the hypotenuse is the walkway, which is 400 yards.
sin(theta) = 200/400
sin(theta) = 1/2
From here, you can find the value of theta by taking the inverse sine (also known as arcsin) of both sides of the equation.
theta = arcsin(1/2)
Using a calculator, you will find that arcsin(1/2) is equal to 30 degrees. So, theta (or feta as mentioned in the question) is 30 degrees.
To summarize, the value of sin(theta) being equal to 1/2 indicates that theta is 30 degrees. The sine function relates the ratios of the sides of a right triangle, and by using the definition of sine, we can find the value of theta.