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Helga [31]
3 years ago
9

David cuts 4 pieces of wood for a birdhouse. When he is done, he realizes that each piece is 2 1/3 inches too short. How does th

e total length of the pieces compare to what their total length should have been? Explain or show how you got your answer
Mathematics
1 answer:
lord [1]3 years ago
4 0

Answer:

Total Length is 9 1/3 inches shorter Than the required length

Step-by-step explanation:

Number of wood pieces cut = 4

Each piece is 2 1/3 inches too short

Total shortage in length :

Number of pieces * shortage per piece

4 * 2 1/3

4 * 7/3

= 28/3 inches = 9 1/3 inches

Hence, The total length of the wood is 9 1/3 inches shorter than the actual or required length of the wood.

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SOLUTION

Let us use a simple diagram to interprete the question

In the diagram above, the dark stuff below represents the shadow and the rectangular bar represents the building. I have labelled the height of the building as h.

So we will use the right-angled triangle formed to find h

As we can see h represents the opposite side and 56.5 feet represents the adjacent side of the right-angle triangle. So we will use TOA

\text{TOA tan }\theta=\frac{opposite}{\text{adjacent}}

So we have

\begin{gathered} \text{ tan }\theta=\frac{opposite}{\text{adjacent}} \\ \text{ tan }61.7\degree=\frac{h}{56.5} \\ 1.8572015=\frac{h}{56.5} \\ \text{cross multiplying, we have } \\ h=1.8572015\times56.5 \\ h=104.931887 \end{gathered}

Hence the answer is 104.9 feet to the nearest tenth

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