Can someone check my answers?
Find # of triangles possible:
<A=44.3, a=11.5, b=7.7
...
2 triangles, B=~27.9 or B=~152.1
<A=29.3, b=20.5, a=12.8
...
2 triangles, B=~51.6 or B=~128.4
#1 only 1 triangle possible because 152+44>180
To check if the given sets of side lengths can form a triangle, you can apply the triangle inequality theorem. According to this theorem, for a triangle with side lengths a, b, and c:
- The sum of any two sides must be greater than the length of the third side.
Let's now check each case:
1. For <A = 44.3, a = 11.5, and b = 7.7:
- The sum of a and b is 11.5 + 7.7 = 19.2, which is greater than the length of the third side.
- The sum of a and c would be 11.5 + 44.3 = 55.8, which is greater than the length of the remaining side.
- However, if we calculate the sum of b and c (7.7 + 44.3), we get 52, which is less than the length of the third side. Therefore, a triangle cannot be formed.
2. For <A = 29.3, b = 20.5, and a = 12.8:
- The sum of a and b is 12.8 + 20.5 = 33.3, which is greater than the length of the third side.
- The sum of a and c is 12.8 + 29.3 = 42.1, which is greater than the length of the remaining side.
- Additionally, the sum of b and c (20.5 + 29.3) is 49.8, which is also greater than the length of the third side.
- Based on the triangle inequality theorem, a triangle can be formed.
In both cases, it is possible to form a triangle with the given side lengths. As for the number of triangles possible, each case has two possible triangles because there are two different possible values for angle B. In the first case, B can be approximately 27.9 degrees or 152.1 degrees. In the second case, B can be approximately 51.6 degrees or 128.4 degrees.