Two corners of a triangle have angles of # ( pi )/ 2 # and # ( pi ) / 6 #. If one side of the triangle has a length of # 8 #, what is the longest possible perimeter of the triangle?
By signing up, you agree to our Terms of Service and Privacy Policy
To find the longest possible perimeter of the triangle given that two corners have angles ( \frac{\pi}{2} ) and ( \frac{\pi}{6} ), proceed as follows:
- Identify the third angle of the triangle using the fact that the sum of angles in a triangle is ( \pi ).
- Determine the side lengths of the triangle using trigonometric relationships, specifically the sine and cosine functions.
- Use the Law of Sines or Law of Cosines to find the lengths of the other sides of the triangle.
- Calculate the perimeter of the triangle using the lengths of its sides.
- Maximize the perimeter by adjusting the lengths of the sides accordingly.
By following these steps, you can determine the longest possible perimeter of the triangle.
By signing up, you agree to our Terms of Service and Privacy Policy
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.
- What is #x# if the perimeter of a rectangle with sides of #x# and #2x + 6# is #27# in?
- A cube has a surface area of 150 in 2. How long is each side of the cube?
- Two corners of a triangle have angles of #(7 pi ) / 12 # and # (3 pi ) / 8 #. If one side of the triangle has a length of #8 #, what is the longest possible perimeter of the triangle?
- Cups A and B are cone shaped and have heights of #16 cm# and #12 cm# and openings with radii of #6 cm# and #8 cm#, respectively. If cup B is full and its contents are poured into cup A, will cup A overflow? If not how high will cup A be filled?
- The base of a triangular pyramid is a triangle with corners at #(6 ,8 )#, #(2 ,7 )#, and #(7 ,3 )#. If the pyramid has a height of #2 #, what is the pyramid's volume?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7