The formula for converting temperature from Fºto Cº is given below. If the

Charlie is watching hot air balloons. balloon a has risen at a 50° angle. balloon b has risen at a 78° angle. if the distance fr

AfilCa [17]

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

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7 0

2 years ago

What’s 6x-3y=18 in slope int? pls help lol

liraira [26]

Answer:

Using the Slope-intercept form, the slope is - 2.

8 0

3 years ago

What is the equation of the line graphed below?

vesna_86 [32]

Answer:

The answer to your question is: letter B

Step-by-step explanation:

Data

A (-5, 4)

B (4, 1)

Formula

slope = m = $\frac{1 - 4}{4 + 5}$

m = $\frac{-3}{9}$ = $\frac{-1}{ 3}$

Point slope

(y - 4) = $\frac{-1}{3}$ (x + 5)

4 0

3 years ago

Joey is 5 feet tall and casts a 45-foot shadow. A building casts a 270-foot shadow at the same time. How tall is the building?

Cerrena [4.2K]

Answer:

the building is thirty feet tall

Step-by-step explanation:

so make a ratio of shadow to joey

5:45

simplify that to

1:9

so you can now divide 270 by nine

30

the building is thirty feet tall

5 0

3 years ago

PLEASE HELP

irina [24]

Answer:

$12\sqrt{3}$ feet

Step-by-step explanation:

In a 30-60-90 triangle, the ratios of the side lengths of the triangle is $1:\sqrt{3} :2$

Where 1 is the shortest leg, root(3) is the longer leg, and 2 is the hypotenuse.

First we can set x equals to the length of the original pole, and so the shorter leg has a length of x/3 and using the ratio of side lengths, we can find that:

$\frac{x}{3} * \sqrt{3} = \frac{\sqrt{3} x}{3} = 12$

Solving for x, we find that

$x=\frac{36}{\sqrt{3} } = \frac{36 * \sqrt{3} }{\sqrt{3} * \sqrt{3} } = \frac{36 \sqrt{3} }{3} = 12\sqrt{3}$

So the length of the original pole would be $12\sqrt{3}$ feet

If you found this answer helpful, please consider marking it as brainliest, or give it a thanks and a 5 star review. Thanks!

6 0

3 years ago