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3 years ago

Please help

Mathematics

2 answers:

umka2103 [35]3 years ago

8 0

Answer: 21

Step-by-step explanation:

law of cosines states that x^2 = y^2 + z^2 - 2yzcos<X

so x^2 = 21^2 + 4^2 - (2*21*4*cos(80)) = 457 - 29.1729 = 427.8271

x = 20.6840 which rounds to 21

atroni [7]3 years ago

3 0

Answer:

x = 21 (Appropriately)

Step-by-step explanation:

Cosine rule states:

a² = b² + c² - 2ab Cos A

b² = a² + c² - 2ac Cos B

c² = a² + c² - 2ab Cos C

Where:

a, b, c are the side lengths

A,B,C are the angles.

We'll take A, B, C as X, Y, Z

and

a,b,c as x,y,z

LET'S FIRE ON!

From the question:

x = ??

y = 21

z = 4

X = 80°

Therefore:

x² = y² + z² - 2yz Cos X

x² = 21² + 4² - 2*21*4 Cos 80°

x²= 441 + 16 - 168 Cos 80°

x² = 457 - 168 * 0.174

x²= 457 - 29.232

x²= 427.768

x= √ 427.768

x = 20.683

x = 21 (Appropriately)

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$\rule{130}1$

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$\rule{130}1$

☯ $\underline{\boldsymbol{According\: to \:the\: Question\:now :}}$

$:\implies\sf x^2 + (x + 2)^{2} = 514 \\\\\\:\implies\sf x^2 + x^2 + 4x + 4 = 514\\\\\\:\implies\sf 2x^2 + 4x + 4 = 514 \\\\\\:\implies\sf 2x^2 + 4x = 514 - 4\\\\\\:\implies\sf 2x^2 + 4x = 510 \\\\\\:\implies\sf 2x^2 + 4x - 510 = 0\\\\\\:\implies\sf x^2 + 2x - 255 = 0 \:\:\:\:\:\Bigg\lgroup \bf{Dividing\:by\:2}\Bigg\rgroup\\\\\\:\implies\sf x^2 + 17x - 15x - 255 = 0\\\\\\:\implies\sf x(x + 17) - 15(x + 17) = 0\\\\\\:\implies\sf (x + 17) (x - 15)\\\\\\:\implies\sf x = - 17\:or\:x = 15\\\\\\:\implies\underline{\boxed {\sf x = 15}}\:\:\:\:\:\Bigg\lgroup \bf{Positive\:odd\: number}\Bigg\rgroup$