Question

Write a sine equation to represent this scenario.Here is a point at the tip of a windmill blade. The center of the windmill is 6 feet off the ground and the blades are 1.5 feet long.

Answer 1

Step-by-step explanation

We must write a sine equation for the height h of the point w from the ground.

Using the data of the problem, we make the following diagram:

From the diagram, we wee see that the height h of point W from the ground is:

`h=h_0+y=6ft+y.`

Where:

• h_0 = 6ft is the height from the ground to the center of the windmill,

,

• y is the height of point W to the center of the windmill.

We see that height y is the opposite cathetus to angle θ, using trigonometry, we see that:

`y=r*\sin\theta=1.5ft*\sin\theta.`

Where r is the radius of the blade.

Replacing the equation of y in the equation of h, we get:

`h(\theta)=6ft+1.5ft*\sin\theta.`

We have found the equation for the height of point W as a function of the angle θ.

When point W is in the position of the diagram, the angle θ is equal to zero, so we have:

`h(0)=6ft+1.5ft*\sin0=6ft+1.5ft*0=6ft.`Answer

• The equation for the height of point W as a function of the angle θ is:

`h(\theta)=6ft+1.5ft*\sin\theta`

• When W is in the position of the diagram, we have θ = 0, so its height is:

`h(0)=6ft+1.5ft*\sin0=6ft`