A triangle has two corners of angles #pi /12# and #(7pi)/8 #. What are the complement and supplement of the third corner?

Answer 1

#(11pi)/24" and "(23pi)/24#

#"the third angle of the triangle is"#
#pi-(pi/12+(7pi)/8)=pi-(23pi)/24=pi/24#
#• " complementary angles sum to "pi/2#
#"complement of "pi/24=pi/2-pi/24=(12pi)/24-pi/24=(11pi)/24#
#• " supplementary angles sum to "pi#
#"supplement of "pi/24=pi-pi/24=(23pi)/24#
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

Complementary angle is #(11pi)/24#

Supplementary angle is #(23pi)/24#

All angles sum to #pi#

Third angle is:

#pi-(pi/12+(7pi)/8)#
#pi-(23pi)/24=pi/24#
An angle and its complement add up to #pi/2 #
#(pi)/24+theta=pi/2=>theta=(11pi)/24#
An angle and its supplement add up to #pi#
#pi/24+theta=pi=>theta=pi-pi/24=(23pi)/24#
#:.#
Complementary angle is #(11pi)/24#
Supplementary angle is #(23pi)/24#
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 3

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} ).

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
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.

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.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7