# A triangle has two corners with angles of # ( pi ) / 3 # and # ( pi )/ 6 #. If one side of the triangle has a length of #5 #, what is the largest possible area of the triangle?

Area of the largest possible triangle is

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

The largest possible area of the triangle can be found using the formula for the area of a triangle: ( A = \frac{1}{2} \times b \times h ), where ( b ) is the base of the triangle and ( h ) is the corresponding height. Given that one side of the triangle has a length of 5, this side can be considered as the base. The height of the triangle can be determined using trigonometric ratios.

Since we know two angles of the triangle (( \frac{\pi}{3} ) and ( \frac{\pi}{6} )), we can find the third angle by subtracting the sum of the given angles from ( \pi ). Then, we can use trigonometric ratios to find the height of the triangle corresponding to the base.

With the base and height, we can calculate the area 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.

- Trapezoid RSTV had median UK. If VT= #4x-6# and UK = #3x+2# and RS = #x+12#, find #x#?
- A right triangle with a hypotenuse of 34 cm and a minor cathetus 16 of cm rotates 360° about the major cathetus. What shape does it form? How do you calculate the surface area and volume of the shape it forms?
- The base of a triangular pyramid is a triangle with corners at #(6 ,2 )#, #(3 ,1 )#, and #(4 ,2 )#. If the pyramid has a height of #8 #, what is the pyramid's volume?
- A chocolate is made in the shape of a sphere of diameter #4cm#, which has hollow inside of diameter #3.7cm#. What is the volume of the chocolate?
- A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is #33 # and the height of the cylinder is #4 #. If the volume of the solid is #25 pi#, what is the area of the base of the cylinder?

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