Question

find the length of b
C side is 30
B side is 78
what is the number for b side

48



72

83.6

108

Answer 1

To find the length of side b, we can use the triangle inequality theorem or properties of triangles, as you have given it in the contexts like sides of a triangle.

Given:
- Side C = 30
- Side B = 78
- We need to find the value of side b.

To analyze the options you provided, let's check the possible values of b against the triangle inequalities:

1. \( a + b > c \) (where a is b and c is 30)
2. \( a + c > b \)
3. \( b + c > a \)

Since we are not given sides explicitly, let's analyze one by one with respect to B and C set.

Since C = 30 and B = 78, let’s verify the conditions using the following potential values for b.

1. **If b = 48**:
- 78 + 48 > 30 → 126 > 30 (True)
- 78 + 30 > 48 → 108 > 48 (True)
- 48 + 30 > 78 → 78 > 78 (False)

2. **If b = 72**:
- 78 + 72 > 30 → 150 > 30 (True)
- 78 + 30 > 72 → 108 > 72 (True)
- 72 + 30 > 78 → 102 > 78 (True)

3. **If b = 83.6**:
- 78 + 83.6 > 30 → 161.6 > 30 (True)
- 78 + 30 > 83.6 → 108 > 83.6 (True)
- 83.6 + 30 > 78 → 113.6 > 78 (True)

4. **If b = 108**:
- 78 + 108 > 30 → 186 > 30 (True)
- 78 + 30 > 108 → 108 > 108 (False)
- 108 + 30 > 78 → 138 > 78 (True)


The only value that satisfies all inequalities is **b = 72**.

So, the length of side b is **72**.