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Helga [31]
3 years ago
8

Ms. Klein wants to put a fence around her garden. The garden is in the shape of a semi-circle with a radius of 12 feet. How much

fence does Ms. Klein need to buy for her garden?
Mathematics
1 answer:
sukhopar [10]3 years ago
5 0

Answer:

P = 61.70 feets

Step-by-step explanation:

Based on the information given :

For fencing , We need to calculate the perimeter of the semicircle ;

Perimeter of a semicircle is given as :

P = πr + 2r

P = perimeter ; r = Radius = 12 feets

P = 12π + 2*12

P = 12π + 24

P = 61.699111 feets

P = 61.70 feets

To. Obtain how much.

We multiply the perimeter by the cost per feet.

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Marty is asked to draw triangles with side lengths of 4 units and 2 units, and a non-included angle of 30°. Select all the trian
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Answer:

The drawn in the attached figure

see the explanation

Step-by-step explanation:

<em>First case</em>

In the triangle ABC

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a=4\ units\\b=2/ units\\B=30^o

Applying the law of sines

Find the measure of angle A

\frac{a}{sin(A)}=\frac{b}{sin(B)}

substitute the given values

\frac{4}{sin(A)}=\frac{2}{sin(30^o)}

sin(A)=1

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A=90^o

Find the measure of angle C

In a right triangle

we know that

B+C=90^o ----> by complementary angles

B=30^o

therefore

C=60^o

Find the length side c

Applying the law of sines

\frac{c}{sin(C)}=\frac{b}{sin(B)}

substitute the given values

\frac{c}{sin(60^o)}=\frac{2}{sin(30^o)}

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therefore

The dimensions of the triangle are

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a=4\ units\\b=2\ units\\c=2\sqrt{3}=3.46\ units

<em>Second case</em>

In the triangle ABC

Let

a=4\ units\\b=2/ units\\A=30^o

Applying the law of sines

Find the measure of angle B

\frac{a}{sin(A)}=\frac{b}{sin(B)}

substitute the given values

\frac{4}{sin(30^o)}=\frac{2}{sin(B)}

sin(B)=0.25

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using a calculator

B=14.48^o

Find the measure of angle C

we know that

The sum of the interior angles in any triangle must be equal to 180 degrees

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A+B+C=180^o

A=30^o\\B=14.48^o

therefore

30^o+14.48^o+C=180^o

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Applying the law of sines

\frac{c}{sin(C)}=\frac{a}{sin(A)}

substitute the given values

\frac{c}{sin(135.52^o)}=\frac{4}{sin(30^o)}

c=5.61\ units

therefore

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A=30^o

B=14.48^o

C=135.52^o

a=4\ units\\b=2\ units\\c=5.61\ units

see the attached figure to better understand the problem

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