Morana is trolling for salmon in Lak Ontario. She sets the fishing rod so its tip is 1 m above the water and the line enters the water at an angle of 45 degrees. Fish have been tracked at a depth of 45km. What length of line must she let out?

*35 degrees

Surely you mean a depth of 45m, not 45km! Draw a diagram. The length x of fishing line can be found via

(45+1)/x = sin35°

To determine the length of line Morana needs to let out for trolling salmon, we can use basic trigonometry.

Let's break down the situation:

1. The fishing rod tip is 1 meter above the water: This signifies the height (opposite side) of a right triangle that can be formed.

2. The line enters the water at an angle of 45 degrees: This gives us the angle between the rod and the line, which is also the angle in our right triangle.

3. Fish have been tracked at a depth of 45 km: This represents the hypotenuse of our right triangle.

To find the length of the line, we can use the trigonometric function known as the tangent (tan) function, which relates the opposite side to the adjacent side in a right triangle.

In this case, the tangent of the angle is equal to the height (1 meter) divided by the length of the line we want to find (let's call it 'x'):

tan(45 degrees) = 1 meter / x

Now, let's solve for 'x' by rearranging the equation:

x = 1 meter / tan(45 degrees)

To calculate this, we need to convert the angle from degrees to radians, as most programming languages and calculators typically operate in radians. We can use the formula: radian = (degree * pi) / 180

tan((45 * pi) / 180) = 1 meter / x

Now, let's calculate the value of 'x':

x = 1 meter / tan((45 * pi) / 180)

Using the value of π (pi) as approximately 3.14159, we can substitute and compute the result.

Fish at a depth of 45 km in Lake Ontario ????

I live about 45 minutes from Lake Ontario, and let me guarantee you that lake is not that deep, lol.

Anyway .....
I will assume you meant 45 m.
let the line be l m long
cos 45 = 46/l ----- ( 1 m above the water + 45 l = 46 m)

l = 46/cos45= appr 65.1 m