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Reptile [31]
3 years ago
10

caleb and emily are standing 100 yards from each other. caleb looks up at a 45 degree angle to see a hot air balloon. Emily look

s yup at a 60 degree angle to see the same hot air ballon. approximate how far is the hot air ballon off the ground?

Mathematics
2 answers:
Sunny_sXe [5.5K]3 years ago
8 0
Check the picture below.

thus then

\bf \begin{cases}
y=100-a\\
y=a\sqrt{3}
\end{cases}\implies 100-a=a\sqrt{3}\implies 100=a+a\sqrt{3}
\\\\\\
100=a(1+\sqrt{3})\implies \boxed{\cfrac{100}{1+\sqrt{3}}=a}
\\\\\\
\textit{what is the altitude \underline{y} then?}\qquad y=100-a
\\\\\\
y=100-\cfrac{100}{1+\sqrt{3}}\implies y\approx 63.39745962156~yards

-Dominant- [34]3 years ago
8 0

Answer:

63.4 Yards

Step-by-step explanation:

B.

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<h3>Answers:</h3>

W(-2,-1) \to \\W \ ' \ (-4,4)\\\\X(0,2) \to \\X \ ' \ (0,4)\\\\Y(3,-1) \to \\Y \ ' \ (6,-2)\\\\V(-2,-1) \to \\V \ ' \ (-4,-2)\\\\

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Explanation:

The scale factor is 2, which means we double each coordinate of each point. The general rule is (x,y) \to (kx,ky) with k = 2. So we can say the more specific dilation rule is (x,y) \to (2x,2y)

Something like W(-2,2) moves to W ' (-4, 4) after multiplying each coordinate by 2. Do the same for the other points as well.

The given preimage points

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will dilate to the corresponding image points

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  • W ' = (-4, 4)
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as shown below. This causes the image to be larger compared to the preimage (since the scale factor is larger than 1). Any given point is twice as far from the origin as compared to before, which in turn means the distance between any two points is twice as much.

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