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Nimfa-mama [501]
3 years ago
7

A tree that is 40 feet tall casts a 30-foot shadow. At the same time, another tree casts a 20-foot shadow. How tall is the secon

d tree?
Mathematics
2 answers:
Olegator [25]3 years ago
7 0
So the tree is 40 ft and then the shadow is 30 so then do 40 -30 = 10 ft difference so then for the second tree do 20 + 10 = 30 ft because the 10 ft difference so the answer is 30 ft tall
charle [14.2K]3 years ago
5 0

Answer:

The second tree is 26.67 foot tall.

Step-by-step explanation:

A tree that is 40 feet tall casts a 30-foot shadow.

\texttt{Ratio of original height to shadow height =}\frac{40}{30}\\\\\texttt{Ratio of original height to shadow height =}\frac{4}{3}

Now we need to find original height of a tree whose shadow is 20 foot.

Original height = Ratio of original height to shadow height x Height of shadow

\texttt{Original height = }\frac{4}{3}\times 20=26.67foot

The second tree is 26.67 foot tall.

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angles formed by these tosses are  79.45, 59.02 and 41.53 degrees to the nearest hundredth.

<u>Step-by-step explanation:</u>

Here , We have a triangle with sides of length 8.6 feet, 5.8 feet and 7.5 feet.

The Law of Cosines (also called the Cosine Rule) says:

c^2 = a^2 + b^2 - 2ab (cosx)

Using the Cosine Rule to find the measure of the angle opposite the side of length 8.6 feet:

⇒ c^2 = a^2 + b^2 - 2ab (cosx)

⇒ c^2 -a^2 - b^2 = -2ab (cosx)

⇒ (cosx) =\frac{ c^2 -a^2 - b^2}{ -2ab}

⇒ (cosx) =\frac{(8.6^2 - 5.8^2 - 7.5^2)}{ ( -2(5.8)7.5)}

⇒ (cosx) =0.18310

⇒ cos^{-1}(cosx) = cos^{-1}(0.18310)

⇒ x = 79.45

The Law of Sines (or Sine Rule) is very useful for solving triangles:

\frac{a}{sin A} = \frac{ b}{sin B} =  \frac{c}{sin C}

We can now find another angle using the sine rule:

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⇒sin Y = \frac{(7.5 (sin 79.45))}{  8.6}

⇒Y = 59.02 degrees

So, the third angle =180 - 79.45 - 59.02 = 41.53 degrees.

Therefore, angles formed by these tosses are  79.45, 59.02 and 41.53 degrees to the nearest hundredth.

4 0
3 years ago
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