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Artemon [7]
2 years ago
12

Use the Law of Cosines to determine the length of the third side of the triangle.

Mathematics
1 answer:
Alchen [17]2 years ago
6 0

<u>Corrected Question</u>

Given a triangle with two sides 4.1 cm and 6.7cm and an Included angle of 35^\circ. Use the Law of Cosines to determine the length of the third side of the triangle.

Answer:

(D) 4.1cm

Step-by-step explanation:

Given a triangle with two sides 4.1 cm and 6.7 cm and an included angle of 35^\circ.

Using Law of Cosines

a^2=b^2+c^2-2bc\cos A\\a^2=4.1^2+6.7^2-2*4.1*6.7\cos 35^\circ\\a^2=16.6958\\a=\sqrt{16.6958}\\a=4.09\\a \approx 4.1$ cm

The correct option is D.

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3 years ago
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The raised vegetable garden in Susan's yard is in the shape of a rectangular prism with a volume of 48 cubic feet and a height o
Anna11 [10]
The correct question is
The raised vegetable garden in Susan's yard is in the shape of a rectangular prism with a volume of 48 cubic feet and a height of 3/4 foot. <span>The base of the rectangular prism is not a square and the width is greater than 2 feet. What is the length and width of the rectangular prism?

let
x-------> the length of the base of the rectangular prism
</span>y-------> the width of the base of the rectangular prism
<span>
we know that
volume of the prism=area of the base*height 
volume=48 ft</span>³
<span>height of the prism=3/4 ft

area of the base=volume/height--------> 48/(3/4)---> 48*4/3----> 64 ft</span>²
<span>
area of the base=64 ft</span>²
<span>area of the base=x*y
64=x*y--------> equation 1

y=x+2--------> equation 2

substitute equation 2 in equation 1
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<span>
using a graph tool----> to resolve the second order equation
see the attached figure

the solution is
x=7.062 ft
y=x+2-----> y=7.062+2-----> y=9.062 ft

the answer is
</span>the length of the base of the rectangular prism is 7.062 ft
the width of the base of the rectangular prism is 9.062 ft<span>
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4 0
3 years ago
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Nat2105 [25]

Answer:

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Step-by-step explanation:

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The equation becomes

1/sin(x) = -1

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x = -90°

x is negative in the third and 4th interval

Third interval;

x = 180+90

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x = 3pi/2

Since the angle should be within 3pi < x < 4pi

Add 2pi to the angle

x = 2pi+ 3pi/2

x = 7pi/2

Hence the required angle is 7pi/2

8 0
3 years ago
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Sladkaya [172]

Answer:

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Step-by-step explanation:

2^4 × 2^6 ÷ 2^5

= 2^10 ÷ 2^5

=2^5

8 0
3 years ago
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