Determine the number of triangles that can be formed with the given information.
and if it forms two possible triangles solve all unknown angles and sides
Angle A=116 degrees
a=10
b=11
One.
Assuming you are using the standard notoation that
b is the side opposite angle B etc.
sinB/11 = sin116°/10
sin B = .9886
angle B = appr 81.4° or appr 98.6°
but the latter is not possible since a triangle cannot have 2 obtuse angles
so B = 81.4° is the only angle possible,
thus only one triangle.
I will leave it up to you to find the other angle and side.
but if you add 81.4 (measure of angle B) plus 116 (measure of angle A) you get 197.368 which is over 180 degrees....
so that would make measure of angle C negative which is why I'm confused
Of course you are right, silly of me not to even check for the obvious.
I was too concerned about the two obtuse angles.
c
so....
No such triangle is possible.
thank you so much!!!
To determine the number of triangles that can be formed with the given information, we need to apply the Triangle Inequality Theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, we have side lengths a = 10 and b = 11, and we want to determine the possible number of triangles. To do this, we consider the Triangle Inequality Theorem for side a:
a + b > c
10 + 11 > c
21 > c
Therefore, the length of the third side (c) must be less than 21 units in order to form a triangle.
Now let's check the lengths of the sides for which triangles can be formed:
1. If c is less than 21 units, we can form a triangle using sides a, b, and c.
For the given information, we haven't been provided with the length of the third side. Hence, we cannot determine the exact number of triangles that can be formed.
If we assume that the length of side c is, for example, 15 units, we can proceed to solve for the remaining angles and sides of the triangle.
Using the Law of Cosines, we can find the unknown angle A:
c^2 = a^2 + b^2 - 2ab * cos(A)
15^2 = 10^2 + 11^2 - 2 * 10 * 11 * cos(A)
225 = 100 + 121 - 220 * cos(A)
225 = 221 - 220 * cos(A)
-220 * cos(A) = 4
cos(A) = -4/220
A ≈ 119.46 degrees
Now we can use the Law of Sines to find the remaining unknown angles B and C:
sin(A)/a = sin(B)/b
sin(119.46 degrees)/10 = sin(B)/11
sin(B) = 11 * sin(119.46 degrees)/10
B ≈ arcsin(11 * sin(119.46 degrees)/10)
To find angle C, we can use the fact that the sum of the angles in a triangle is 180 degrees: C = 180 - A - B.
With these calculations, we can solve for the unknown angles B and C and find all the unknown sides of the triangle.