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sdas [7]
2 years ago
10

David proved the Law of Cosines with reference to ∆ABC using a different method. Arrange the steps of his proof in the correct s

equence. In , (Pythagorean Theorem) In , (Pythagorean Theorem) (on simplification) (Transitive Property) Therefore, . Similarly, prove that and . (on simplification) (on simplification) Draw a perpendicular, , from B to side AC. Let and . Therefore, .

Mathematics
1 answer:
AURORKA [14]2 years ago
3 0

Answer: We can arrange the steps with help of below explanation.  

Step-by-step explanation:

Here ABC is a triangle,

Draw a perpendicular from BD to side AC ( construction)

where D\in AC

In the right triangle BCD, from the definition of cosine:

cos C =CD/ BC

CD= a cos C

Subtracting this from the side b, we see that

DA= b-acos C  

In the triangle BCD, from the definition of sine:

sin C =BD  / a

BD = a sin C  

In the triangle ADB, applying the Pythagorean Theorem

c^2  =BD^2 +DA^2  

Substituting for BD and DA from (2) and (3)

c^2 =(asinC)^2 +(b-acosC)^2  

⇒c^2 =a^2sin ^2C+b^2-2ab cosC+a^2 cos ^2C   ( On simplification)

⇒c^2 =a^2sin ^2C+a^2 cos ^2C+b^2-2abcos C

⇒c^2=a^2(sin^2C+cos^2C) +b^2-2abcosC

⇒c^2 = a^2+b^2-2abcosC (because,sin^2\theta+cos^2\theta =1 )


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Mashutka [201]

Answer:

0

Step-by-step explanation:

f(x) = √(x) + 12

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5 0
2 years ago
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Answer:

  • The arcs on the Golden Gate Bridge.

Explanation:

I think about the Golden Gate Bridge, which is a suspension bridge.

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The x-intercept is a point on the x-axis.
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7 0
2 years ago
Eliza brought 3 pans of homemade fruit bars to school. Her classmates ate 7/12 of each pan. Eliza gave 1 whole pan of the leftov
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