Draw and solve any triangles satisfying alpha = 20 degrees

b = 10
c = 16

Using the law of cosines (and assuming alpha is between b and c), then

a^2 = 10^2+16^2-2 * 10*16 * cos 20

a^2 = 356 - 320 * cos 20

Figure out cos 20, we get roughly 0.93969262078

we plug this in to get roughly 55.2983614 for side a.

I don't know what else you mean....

To draw and solve a triangle given specific measurements, we first need to understand what each measurement represents. In this case, we have:

- α (alpha) = 20 degrees: This represents one of the angles in the triangle.
- b = 10: This represents the length of the side opposite to angle α.
- c = 16: This represents the length of another side of the triangle.

Now, let's start by drawing the triangle. Since we know two side lengths and one angle, we can use the Law of Sines to solve for the remaining side and angles.

1. Start by drawing a horizontal line segment for the base of the triangle. Label the endpoints as A and B.

B
_______
A C

2. From point A, construct an angle α = 20 degrees.

α
_______
A C B

3. Measure a distance of b = 10 from point A along the line segment and mark it as point D.

α
_______
A C B
D

4. From point D, construct a line segment with length c = 16 towards the right.

α
_______
A C B
D--------
C

5. Connect points C and B to form the remaining sides of the triangle.

α
_______
A C B
D--------
b c

Now that we have drawn the triangle, we can solve for the remaining side and angles using the Law of Sines.

The Law of Sines states that in any triangle:

a/sin(A) = b/sin(B) = c/sin(C)

Since we know b = 10 and C = 20 degrees, we can use the equation to solve for a:

a/sin(A) = b/sin(B)
a/sin(A) = 10/sin(180 - A - B) (Since A + B + C = 180 degrees)
a/sin(A) = 10/sin(180 - A - 20)
a/sin(A) = 10/sin(160 - A)

Now, we can solve this equation for a by cross-multiplying:

a * sin(160 - A) = 10 * sin(A)

Finally, we solve for a by dividing both sides by sin(160 - A):

a = (10 * sin(A)) / sin(160 - A)

Plugging in A = 20 degrees, we can calculate the value of a, which will allow us to completely solve the triangle.