A triangle has two corners with angles of # ( pi ) / 2 # and # ( pi )/ 6 #. If one side of the triangle has a length of #4 #, what is the largest possible area of the triangle?
Largest possible area of the right
Three angles are It is a right triangle with angles 30, 60, 90 and the sides will be in the ratio of 1 : To get the largest are, side 4 should correspond to the least angle Three sides will be Largest possible area of the right
By signing up, you agree to our Terms of Service and Privacy Policy
To find the largest possible area of the triangle, we can use the formula for the area of a triangle:
Area = 1/2 * base * height
Since we know one side of the triangle is 4 units long, let's call this side the base. The height of the triangle will be the distance from the opposite vertex (the one not on the 4-unit side) to the base.
To find the height, we can use trigonometry. Since we know the angles of the triangle are π/2 and π/6, we can find the height using the sine of π/6.
sin(π/6) = opposite/hypotenuse
We can rearrange this to find the height:
height = sin(π/6) * hypotenuse
Since the hypotenuse of the right triangle formed by the height is the side opposite to the right angle (which is the base, 4 units), the hypotenuse is also 4 units.
So, height = sin(π/6) * 4
Now, we can plug the values of base and height into the formula for the area of a triangle:
Area = 1/2 * 4 * sin(π/6) * 4
Area = 1/2 * 4 * (1/2) * 4
Area = 8
Therefore, the largest possible area of the triangle is 8 square units.
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.
- Two corners of a triangle have angles of #(3 pi ) / 8 # and # pi / 12 #. If one side of the triangle has a length of #9 #, what is the longest possible perimeter of the triangle?
- A pyramid has a parallelogram shaped base and a peak directly above its center. Its base's sides have lengths of #2 # and #7 # and the pyramid's height is #6 #. If one of the base's corners has an angle of #pi/4 #, what is the pyramid's surface area?
- A circle is inscribed in a square, which means that each side of the square touches the circle at exactly one point. If the area of the circle is 144pi, what is the length of the diagonal?
- A cone has a height of #5 cm# and its base has a radius of #4 cm#. If the cone is horizontally cut into two segments #1 cm# from the base, what would the surface area of the bottom segment be?
- An ellipsoid has radii with lengths of #5 #, #5 #, and #8 #. A portion the size of a hemisphere with a radius of #3 # is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

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