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Kisachek [45]
3 years ago
8

Kim is building a triangular dog pen. She will use an existing 10 m wall as one side. She will then build a fence going out at a

45°
angle on one side of the wall and a 65° angle on the other side. How much chain-link fence is needed to complete the fence?
es )

Mathematics
2 answers:
Tema [17]3 years ago
8 0

Answer:

  17.2 ft

Step-by-step explanation:

The angle that the fence makes opposite the wall is ...

  180° -45° -65° = 70°

The law of cosines can be used to find the lengths of fence needed.

The fence opposite the 45° angle will have a length of ...

  short side = (10 ft)·sin(45°)/sin(70°) = 7.525 . . . feet

The fence opposite the 65° angle will have a length of ...

  long side = (10 ft)·sin(65°)/sin(70°) = 9.645 . . . feet

Then the total length of fence required is ...

  7.525 ft +9.645 ft = 17.170 ft

About 17.2 feet of chain-link fence is required to complete the enclosure.

_____

We have assumed there is no chain-link fence along the 10 ft wall.

_____

The Law of Sines tells you that for sides a, b, c and opposite angles A, B, C, you have ...

  a/sin(A) = b/sin(B) = c/sin(C)

For some given side 'a' and opposite angle A, the other two sides can be found from their opposite angles as ...

  b = sin(B)·a/sin(A)

  c = sin(C)·a/sin(A)

expeople1 [14]3 years ago
7 0
The correct answer would 27.2 m
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Given the perimeter and length of the garden, the width of the garden was extended by 4 feet

<h3>How to find width of the garden</h3>

  • Length of the garden = 12 feet
  • Width of the garden = 7 feet

  • Width extension =( 7 + w) feet

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Perimeter = 2(length+ width)

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brainly.com/question/24571594

4 0
2 years ago
26. Students who take a statistics course are given a pre-test on the concepts and skills for the first chapter of a statistics
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The test statistic value lies to the right of the critical value. So we have sufficient evidence to reject the null hypothesis.

<h3>What are null hypotheses and alternative hypotheses?</h3>

In null hypotheses, there is no relationship between the two phenomenons under the assumption or it is not associated with the group. And in alternative hypotheses, there is a relationship between the two chosen unknowns.

Students who take a statistics course are given a pre-test on the concepts and skills for the first chapter of a statistics course.

Then they are given a post-test once the professor has concluded lecturing on the material.

Pre-test and post-test scores for 4 students in an elementary statistics class are given below.

Then we have

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The test statistic value is given by

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Since the test statistic value lies to the right of the critical value. So we have sufficient evidence to reject the null hypothesis.

Hence, we can conclude that \mu _d > 0 that is test scores have improved.

More about the null hypotheses and alternative hypotheses link is given below.

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