All categories

3 years ago

You are standing 30 meters from a hot air balloon that is preparing to take

Mathematics

1 answer:

Lerok [7]3 years ago

8 0

Answer:

The distance to the top of the balloon is approximately 33.977 meters

Step-by-step explanation:

The (horizontal) distance from the hot air balloon from the observer, l = 30 m

The angle of elevation to the top of the balloon, θ = 28°

With the balloon standing upright, the distance to the top of the balloon, d, the height of the balloon, h and the horizontal distance to the balloon, l, form a right triangle, where;

d = The hypotenuse side

l = The leg adjacent to the reference (given) angle,

h = The leg opposite to the given angle, θ

By trigonometric ratios, we have;

$cos\angle X = \dfrac{Adjacent\ leg \ length}{Hypotenuse \ length}$

From which we get;

$cos\angle \theta = \dfrac{l}{d}$

$cos(28^{\circ}) = \dfrac{30 \ m}{d}$

$d = \dfrac{30 \ m}{cos(28^{\circ}) } \approx 33.977 \, m$

The distance to the top of the balloon, d ≈ 33.977 m

You might be interested in

2x+4y=-12 and -4x-2y=-12 what is the solution

DochEvi [55]

Answer:

The answer is that x = 6 and y = -6

Step-by-step explanation:

In order to find these values, we can use elimination. To do so, we multiply the first equation by 2 and then add the equations together.

4x + 8y = -24

-4x - 2y = -12

------------------

6y = -36

y = -6

Now that we have this value, we can plug the value into one of the originals and find x.

2x + 4y = -12

2x + 4(-6) = -12

2x - 24 = -12

2x = 12

x = 6

4 0

3 years ago

PLEASE HELP WILL GIVE BRAINLIEST!!!

suter [353]

Answer:

Vertical Angles Theorem

Step-by-step explanation:

The two triangles will be equal by SAS

3 0

3 years ago

A polygon is regular when all angles are equal and all sides are equal True or False

Vesna [10]

Answer:

True

Step-by-step explanation:

True, because a polygon have all angles that are equal and all lengths are the same length.

4 0

3 years ago

Explain what is meant by a 100% decrease.

dsp73

So lets say u have 100$ and it decreases by 100% u would have no money left

7 0

3 years ago

Write an equation that has a graph with the shape of y = x^2, but shifted left 3 units.

svetoff [14.1K]

$\bf \qquad \qquad \qquad \qquad \textit{function transformations}
\\ \quad \\\\
% left side templates
\begin{array}{llll}
f(x)=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
y=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
f(x)=&{{ A}}\sqrt{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}}(\mathbb{R})^{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}} sin\left({{ B }}x+{{ C}} \right)+{{ D}}
\end{array}\\\\
--------------------\\\\$

$\bf % template detailing
\bullet \textit{ stretches or shrinks horizontally by } {{ A}}\cdot {{ B}}\\\\
\bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}
\\\\
\bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\
\left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\
\left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\$

$\bf \bullet \textit{ vertical shift by }{{ D}}\\
\left. \qquad \right. if\ {{ D}}\textit{ is negative, downwards}\\\\
\left. \qquad \right. if\ {{ D}}\textit{ is positive, upwards}\\\\
\bullet \textit{ period of }\frac{2\pi }{{{ B}}}$

now, with that template in mind, let's see

$\bf y=x^2\implies 
\begin{array}{llll}
y=(&1x&-0)^2\\
&B&C
\end{array}$

so, just change C to +3, thus C/B is 3/1

6 0

3 years ago