A triangle has two corners with angles of # pi / 6 # and # (3 pi )/ 8 #. If one side of the triangle has a length of #12 #, what is the largest possible area of the triangle?
Largest possible area of the triangle is 131.9005
The remaining angle:
I am assuming that length AB (12) is opposite the smallest angle.
Using the ASA
By signing up, you agree to our Terms of Service and Privacy Policy
To find the largest possible area of the triangle, use the formula for the area of a triangle:
[A = \frac{1}{2} \times b \times h]
where (b) is the base and (h) is the height. The base of the triangle is the side with length 12.
To find the height, use the formula for the height of a triangle:
[h = b \times \sin(\theta)]
where (\theta) is the angle opposite the base.
Given the angles (\pi/6) and (3\pi/8), the angle opposite the base is (\pi/6) or (3\pi/8).
So, calculate the height for both cases:
For (\theta = \pi/6): [h_1 = 12 \times \sin(\pi/6) = 12 \times \frac{1}{2} = 6]
For (\theta = 3\pi/8): [h_2 = 12 \times \sin(3\pi/8)]
Now, find the larger area between the two cases.
[A_1 = \frac{1}{2} \times 12 \times 6]
[A_2 = \frac{1}{2} \times 12 \times h_2]
Compare (A_1) and (A_2) to find the larger area.
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 the area of a rectangle ABCD with these vertices: A (-2, -5), B (-2, 5), C (6, 5) D (6, -5)?
- What is the surface area of an icosahedron as a function of its radius?
- How do you find the area of an equilateral triangle given the perimeter?
- An ellipsoid has radii with lengths of #9 #, #12 #, and #10 #. A portion the size of a hemisphere with a radius of #5 # is removed form the ellipsoid. What is the remaining volume of the ellipsoid?
- Explain how the formula for the area of a trapezoid can be used to find the formulas for the areas of parallelograms and triangles?

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