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Sveta_85 [38]
3 years ago
11

The exact value of tan 5 π/12

Mathematics
1 answer:
Annette [7]3 years ago
7 0

Answer:

C

Step-by-step explanation:

Using the addition formula for tangent

tan(x + y) = \frac{tanx+tany}{1-tanxtany} and the exact values

tan(\frac{\pi }{6} ) = \frac{1}{\sqrt{3} } and tan(\frac{\pi }{4} ) = 1

tan(\frac{5\pi }{12} ) = tan(\frac{\pi }{6} + \frac{\pi }{4} )

= \frac{tan(\frac{\pi }{6})+tan(\frac{\pi }{4})  }{1-tan(\frac{\pi }{6})tan(\frac{\pi }{4})  }

= \frac{\frac{1}{\sqrt{3} }+1 }{1-\frac{1}{\sqrt{3} }.1 }  ( multiply numerator/ denominator by \sqrt{3} )

= \frac{1+\sqrt{3} }{\sqrt{3} -1}

rationalise denominator by multiplying numerator/denominator by (\sqrt{3} + 1)

= \frac{(1+\sqrt{3})(\sqrt{3}+1)  }{(\sqrt{3}-1)(\sqrt{3}+1)  }

= \frac{\sqrt{3}+1+3+\sqrt{3}  }{3-1}

= \frac{2\sqrt{3}+4 }{2}

= \sqrt{3} + 2 → C

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Frank got a gift for his sister and put it in a shoebox.
Leona [35]

Answer:

The correct answer is option C.

Step-by-step explanation:

Length of shoe box = l = 11 inches

Width of the shoes box = w = 6 inches

Height of the shoe box = h = 5 inches

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a right pyramid with a square base has a base edge length of 24 feet and slant height of 20 feet what is the height of the pyram
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Let

l-------> the slant height of the right pyramid

b------> the length side of the square base of the right pyramid

h------> the height of the right pyramid

we know that

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l^{2} =h^{2}+(\frac{b}{2})^{2}

Solve for h

h^{2}=l^{2}-(\frac{b}{2})^{2}

in this problem we have

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Substitute in the formula

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Hope this helps :)

Have a nice day!

4 0
3 years ago
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