Explore Westonci.ca, the top Q&A platform where your questions are answered by professionals and enthusiasts alike. Our platform connects you with professionals ready to provide precise answers to all your questions in various areas of expertise. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

DETAILS
MY NOTES
Use the figure of the rectangle shown below to answer the questions. (Note: w and h are lower case.
D
h
11
(a) If the diagonal, D, of the rectangle is 18 feet, express the perimeter of the rectangle as a function of w only.
P(W) =
(b) If the diagonal, D, of the rectangle is 18 feet, express the angle 8 as a function of w only.
0(W) =



DETAILS MY NOTES Use The Figure Of The Rectangle Shown Below To Answer The Questions Note W And H Are Lower Case D H 11 A If The Diagonal D Of The Rectangle Is class=

Sagot :

The perimeter of the rectangle as a function of w only is P(w) = 2[√(324 - w²) + w]

The perimeter of the rectangle P = 2(h + w)

Since the diagonal is D = 18 feet, using Pythagoras' theorem, we have that

D² = h² + w²

So, making h subject of the formula, we have

h = √(D² - w²)

h = √(18² - w²)

h = √(324 - w²)

Since the perimeter of the rectangle P = 2(h + w), substituting the value of h into P, we have

P = 2(h + w)

P = 2[√(324 - w²) + w]

P(w) = 2[√(324 - w²) + w]

So, the perimeter of the rectangle as a function of w only is P(w) = 2[√(324 - w²) + w]

The angle θ as a function of w only is θ(w) = sin⁻¹[w/18]

Using trigonometric functions, sinθ = w/D

since D = 18, substituting the value of D into the equation, we have

sinθ = w/18

Taking inverse tan of both sides, we have

θ = sin⁻¹[w/18]

θ(w) = sin⁻¹[w/18]

So, the angle θ as a function of w only is θ(w) = sin⁻¹[w/18]

Learn more about perimeter of a rectangle here:

https://brainly.com/question/7538991