Which figure appears to be congruent to this triangle?

Mathematics

1 answer:

Margaret [11]3 years ago

7 0

Answer:

probably

D because they're both the same shape it's just D is smaller.

Step-by-step explanation:

1.all three sides are equal

2.2 sides and their included angle are equal

3.A pair of angles and their included side are equal

4.2 corresponding angles and their non included side are equal.

5.the hypotenuse and 1 leg of a right triangle equal.

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Find 2 common angles that sum to (17pi/12) 2. Evaluate tan(17pi/12) using the sum identity for tangent.

Dmitry [639]

Note that
$\frac{17 \pi }{12} = \frac{3 \pi }{12} + \frac{14 \pi }{12} = \frac{ \pi }{4} + \frac{7 \pi }{6}$

Note that
$x= \frac{ \pi }{4}:\,\, sin(x) =cos(x)= \frac{1}{ \sqrt{2} },\,tan(x)=1\\x= \frac{7 \pi }{6} :\,\,sin(x)=- \frac{1}{2} ,\,\,cos(x)=- \frac{ \sqrt{3} }{2} ,\,\,tan(x)= \frac{1}{ \sqrt{3} }$

Use the identity
$tan(x+y)= \frac{tan(x)+tan(y)}{1-tan(x)tan(y)}$

Therefore
$tan( \frac{17 \pi }{12} )= \frac{1+ \frac{1}{ \sqrt{3} } }{1- \frac{1}{ \sqrt{3} } } = \frac{ \sqrt{3}+1 }{ \sqrt{3}-1} = \frac{( \sqrt{3}+1 )^{2}}{( \sqrt{3}-1 )( \sqrt{3}+1 )} = \frac{3+1+2 \sqrt{3}}{3-1} =2+ \sqrt{3}$

Answer: 2 + √3

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Answer:

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Step-by-step explanation:

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