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3 years ago

Trig please help

Mathematics

2 answers:

Olenka [21]3 years ago

6 0

Answer:

One

Step-by-step explanation:

14/sin(54) = 7/sinC

sinC = 0.4045084972

C = 23.86, 156.14

Since 156.14+54 = 210.14 > 180

Only one triangle can be formed with angle 23.86° at C

irinina [24]3 years ago

6 0

Answer:

None (zero)

Step-by-step explanation:

8/sin(70) = 16/sinB

=>sinB = 1.88

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Answer:

$\dfrac{1}{(b-c)},\dfrac{1}{(c-a)} ,\dfrac{1}{(a-b)} are\ in\ AP$

Step-by-step explanation:

Given that $(b-c)^2, (c-a)^2 , (a-b)^2$ are in AP

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$\dfrac{1}{(b-c)},\dfrac{1}{(c-a)} ,\dfrac{1}{(a-b)}2\dfrac{1}{(c-a)} =\dfrac{1}{(b-c)}+\dfrac{1}{(a-b)}\\\\\Rightarrow \dfrac{2}{(c-a)}= \dfrac{a-b+b-c}{(b-c)(a-b)} \\\\\Rightarrow \dfrac{2}{(c-a)}= \dfrac{a-c}{(b-c)(a-b)} \\\\\Rightarrow2(b-c)(a-b) = (c-a)(a-c) \\\\\Rightarrow 2(ab-b^2-ac+bc)= -(a-c)^2\\\\\Rightarrow 2ab- 2b^2-2ac+2bc = -a^2-c^2+2ac\\\\\Rightarrow a^2-2b^2+c^2=4ac-2ab-2bc$

Which is the result of AP

Hence proved

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