Answer:
The volume of the jewelry box will be given by,
Step-by-step explanation:
It is provided that, Jasmine found a wooden jewelry box shaped like a right rectangular prism.
Consider the diagram below for the shape of a right rectangular prism.
The volume of a right rectangular prism is given by the formula:
Here,
l = length of the rectangle
w = width of the rectangle
h = height of the rectangular prism
Thus, the volume of the jewelry box will be given by,
Answer:
h = 3.62
Step-by-step explanation:
First, as both triangles have the same angles we can use the relationship of areas and sides corresponding to similar triangles as follows:
Now we know that the new triangle has sides of 4.18. Then, as these triangles are equilateral we can use the Pythagorean Theorem to find the height:
Finally the height of this new triangle is 3.62 cm
Answer:
θ = (60° )
Step-by-step explanation:
Using the identity
sin²x + cos²x = 1 ⇒ sin²x = 1 - cos²x
Given
cos²θ - sin²θ = 2 - 5cosθ
cos²θ - (1 - cos²θ) = 2 - 5cosθ
cos²θ - 1 + cos²θ = 2 - 5cosθ
2cos²θ - 1 = 2 - 5cosθ ( subtract 2 - 5cosθ from both sides )
2cos²θ + 5cosθ - 3 = 0 ← in standard form
(cosθ + 3)(2cosθ - 1) = 0 ← in factored form
Equate each factor to zero and solve for θ
cosθ + 3 = 0
cosθ = - 3 ← not possible as - 1 ≤ cosθ ≤ 1
2cosθ - 1 = 0
cosθ = , so
θ = (
) =
( or 60° )
Given parameters:
Length of the suitcase = 24 inches
Length of the diagonal = 30 inches
Unknown:
Length of zipper required to cover the perimeter = ?
The length of this zipper is the same as the perimeter of the rectangular suitcase.
Perimeter of a rectangle = 2(L + B)
where L is the length and B is the breadth
Now, let us find the find the unknown breadth;
Using Pythagoras theorem;
30² = 24² + Breadth²
Breadth² = 30² - 24² = 324
Breadth = √324 = 18 inches
Perimeter of the suitcase = 2(24 + 18) = 84 inches.
The length of zipper that will cover this suitcase is 84inches.
