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A triangle has two corners of angles #pi /12# and #(5pi)/8 #. What are the complement and supplement of the third corner?

Answer 1

#(5pi)/24# and #(17pi)/24# respectively.

We know that the sum of 3 angles of a triangle is #pi#.

Now we are given 2 angles of a triangle. So, as to find the remaining third angle, we have #pi - (pi/12) - ((5pi)/8) = (24pi - 2pi - 15pi)/24 = (7pi)/24.#

Complement of this third angle is #pi/2 - (7pi)/24 = (5pi)/24.#

Supplement of the third angle is #pi - (7pi)/24 = (17pi)/24.#

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Answer 2

Mason Adams

The complement of the third angle in the triangle is ( \frac{\pi}{2} - \left(\frac{\pi}{12} + \frac{5\pi}{8}\right) = \frac{11\pi}{24} ). The supplement of the third angle is ( \pi - \left(\frac{\pi}{12} + \frac{5\pi}{8}\right) = \frac{19\pi}{24} ).

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Answer from HIX Tutor

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.