# Two corners of a triangle have angles of # (2 pi )/ 3 # and # ( pi ) / 6 #. If one side of the triangle has a length of # 4 #, what is the longest possible perimeter of the triangle?

Longest possible perimeter = 14.928

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

To find the longest possible perimeter of the triangle, we need to consider the case where the remaining angle is the largest possible. Since the sum of angles in a triangle is always ( \pi ) radians (or 180 degrees), we can find the measure of the third angle by subtracting the given angles from ( \pi ):

[ \text{Third angle} = \pi - \frac{2\pi}{3} - \frac{\pi}{6} ]

Then, we can calculate the perimeter of the triangle using the given side lengths and angles, considering the triangle to be equilateral:

[ \text{Perimeter} = 3 \times \text{side length} ]

Substituting the given side length of 4:

[ \text{Perimeter} = 3 \times 4 ]

[ \text{Perimeter} = 12 ]

Therefore, the longest possible perimeter of the triangle is 12 units.

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

- An ellipsoid has radii with lengths of #12 #, #11 #, and #8 #. A portion the size of a hemisphere with a radius of #8 # is removed form the ellipsoid. What is the remaining volume of the ellipsoid?
- If the radius of a circle is 10 feet, what is the diameter?
- A cone has a height of #9 cm# and its base has a radius of #8 cm#. If the cone is horizontally cut into two segments #3 cm# from the base, what would the surface area of the bottom segment be?
- The perimeter of a rectangular garden is 368 feet. If the length of the garden is 97 feet, what is its width?
- The perimeter of parallelogram CDEF is 54 centimeters. Find the length of segment FC if segment DE is 5 centimeters longer than segment EF? (Hint: Sketch and label a diagram first.)

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