a boat is tied by a rope 12 meters long to a ring that is 3.5 meters above the water.If the rope is taut find the angle it makes with the water?

recall your basic trig functions:

sin x = 3.5/12

To find the angle the rope makes with the water, we can use trigonometry. Let's call the angle "θ".

We have a right triangle formed by the rope, the distance from the ring to the water surface, and the rope connecting the boat to the ring.

In this triangle, the opposite side is the distance from the ring to the water surface, which is given as 3.5 meters, and the hypotenuse is the length of the rope, which is 12 meters.

Using the sine function, we can set up the equation:

sin(θ) = opposite/hypotenuse

sin(θ) = 3.5/12

Now, we can take the inverse sine (sin^-1) of both sides to solve for the angle θ:

θ = sin^-1(3.5/12)

Using a calculator, we get:

θ ≈ 16.89 degrees

Therefore, the angle the rope makes with the water is approximately 16.89 degrees.

To find the angle that the rope makes with the water, we can use trigonometry. Specifically, we can use the sine function to determine the relationship between the angle and the sides of the triangle formed by the rope, the water, and the vertical line connecting the ring and the water.

Let's call the angle that the rope makes with the water "θ" (theta).

In the triangle, we have the opposite side (the vertical distance from the ring to the water), which is 3.5 meters, and the hypotenuse (the length of the rope), which is 12 meters. We need to find the ratio of the opposite side to the hypotenuse, which is sin(θ).

Using the sine function, we have sin(θ) = opposite/hypotenuse = 3.5/12.

To find θ, we can take the inverse sine (also known as arcsine) of both sides: θ = arcsin(3.5/12).

Now, we can use a calculator to find the inverse sine of 3.5/12 and get the angle in radians or degrees, depending on the calculator setting.

Note: In this explanation, we assume that the rope is perfectly straight and not affected by any external forces or slack.

.29