Westonci.ca is your trusted source for finding answers to all your questions. Ask, explore, and learn with our expert community. Discover a wealth of knowledge from experts across different disciplines on our comprehensive Q&A platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.
Sagot :
The distance from Balloon A to Balloon B, d ≈ 1,052 feet
What is distance ?
- Distance is defined to be the magnitude or size of displacement between two positions.
- Note that the distance between two positions is not the same as the distance traveled between them.
- Distance traveled is the total length of the path traveled between two positions. Distance traveled is not a vector.
The given parameters are;
The angle at which Balloon A rises, x° = 50° above horizontal
The angle at which Balloon B rises, y° = 78° above horizontal
The (vertical) distance of Balloon A to the ground, h = 1,000 ft.
The required parameter;
The distance from Balloon A to Balloon B, d
We find the distances of the balloons from Charlie and the angle between the balloon strings, θ, then apply cosine rule
Let,
The height of the balloon strings are equal
The distance of Balloon A to the ground, h₁ = The distance of Balloon B to the ground, h₂ = 1,000 ft.
The distance of the Balloon A from Charlie, l₁, is given as follows;
l₁ × sin(x°) = h₁
∴ l₁ = h₁/(sin(x°))
Which gives;
l₁ = 1,000 ft./(sin(50°)) ≈ 1,305.41 ft.
l₁ ≈ 1,305.41 ft.
For Balloon B, we get;
h₁ = h₂ = 1,000 ft.
∴ l₂ = 1,000 ft./(sin(78°)) ≈ 1,022.34 ft.
l₂ ≈ 1,022.34 ft
The angle between the balloon strings, θ = 180° - (x° + y°)
∴ θ = 180° - (50° + 78°) = 52°
The angle between the balloon strings, θ = 52°
By cosine rule, we have;
d = √(l₁² + l₂² - 2 × l₁ × l₂ × cos(θ))
∴ d = √(1,305.41² + 1,022.34² - 2 × 1,305.41×1,022.34 × cos(52°)) ≈ 1,052 feet
Therefore, the distance from Balloon A to Balloon B, d ≈ 1,052 feet
Learn more about distance
brainly.com/question/15172156
#SPJ4
Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.
