A triangle has two corners of angles #pi /12# and #(7pi)/8 #. What are the complement and supplement of the third corner?
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Complementary angle is Supplementary angle is
Third angle is:
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Given that the triangle has angles of ( \frac{\pi}{12} ) and ( \frac{7\pi}{8} ), we can find the third angle by subtracting the sum of the known angles from ( \pi ), as the sum of the angles in a triangle is always ( \pi ).
Let ( \theta ) be the measure of the third angle. Then:
[ \theta = \pi - \left(\frac{\pi}{12} + \frac{7\pi}{8}\right) ]
[ \theta = \pi - \frac{\pi}{12} - \frac{7\pi}{8} ]
[ \theta = \pi - \frac{8\pi}{24} - \frac{21\pi}{24} ]
[ \theta = \pi - \frac{29\pi}{24} ]
[ \theta = \frac{24\pi}{24} - \frac{29\pi}{24} ]
[ \theta = \frac{-5\pi}{24} ]
The complement of an angle is the difference between the angle and ( \frac{\pi}{2} ), while the supplement is the difference between the angle and ( \pi ).
Therefore, the complement of ( \frac{-5\pi}{24} ) is ( \frac{\pi}{2} - \frac{-5\pi}{24} = \frac{12\pi}{24} + \frac{5\pi}{24} = \frac{17\pi}{24} ), and the supplement is ( \pi - \frac{-5\pi}{24} = \frac{24\pi}{24} + \frac{5\pi}{24} = \frac{29\pi}{24} ).
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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