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k0ka [10]
3 years ago
14

An artist used silver wire to make a square that has a perimeter of 40 inches. She then used copper wire to make the largest cir

cle that could fit in the square, as a shown below
Show work please

Mathematics
1 answer:
rjkz [21]3 years ago
3 0

Answer:

The artist used 8.6 inches more of silver wire

Step-by-step explanation:

Perimeter of the square

P = 4*a

P = 4*a = 40 in

a = 10 in

Each side of the square has a length of 10 in

The diameter of the circle is equal to the length of the side of  the square

Diameter = 10 in

Perimeter of the circle

P_c = 2*π*radius  = π*diameter

P_c = (3.14)*10 in = 31.4 in

Inches of silver wire (square)   =  40 in

Inches of copper wire (circle)   =  31.4 in

40- 31.4  in  = 8.6 in

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Ships A and B are 1,425 feet apart and detect a submarine below them. The angle of depression from ship A to the submarine is 59
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Answer: The distance from ship B to the submarine is 1270.68 feet and the distance from ship A to the submarine is 1084.18 feet.

Step-by-step explanation:

Since we have given that

Distance between Ships A and B = 1425 feet

Angle of depression from ship A to the submarine =59°

Angle of depression from ship B to the submarine = 47°

As shown in the figure below:

Remaining angle will be

180\textdegree-(47\textdegree+59\textdegree)\\\\=180\textdegree-106\textdegree\\\\=74\textdegree

So, we will use "Sine formula ":

\frac{\sin 74\textdegree}{1425}=\frac{\sin 59\textdegree}{B}\\\\B=\frac{1425\times \sin 59\textdegree}{\sin 74\textdegree}\\\\B=1270.68\ feet

Similarly,

\frac{\sin 74\textdegree}{1425}=\frac{\sin 47\textdegree}{A}\\\\A=\frac{1425\times \sin 47\textdegree}{\sin 74\textdegree}\\\\A=1084.18\ feet

Hence, the distance from ship B to the submarine is 1270.68 feet and the distance from ship A to the submarine is 1084.18 feet.

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