<span>Based in the information given in the problem, you must apply the The Angle Bisector Theorem. Let's call the triangle: "ABC"; the internal bisector of the angle that divides its opposite side: "AP"; and "x": the longest and shortest possible lengths of the third side of the triangle.
If BP= 6 cm and CP= 5 cm, we have:
BP/CP = AB/AC
We don't know if second side of the triangle (6.9 centimeters long) is AB or AC, so:
1. If AB = 6.9 cm and AC = x:
6/5 = 6.9/x
x = (5x6.9)/6
x = 5.80 cm
2. If AC= 6.9 cm and AB= x:
6/5 = x/6.9
x = 6.9x6/5
x = 8.30 cm
Then, the answer is:
The longest possible length of the third side of the triangle is 8.30 cm and the and shortest length of it is 5.80 cm.</span>
x = 64°
Step-by-step Explanation
x = 1/2[(360° - 2*58°)-2*58°]
x = 1/2[(360° - 2*58°) - 2*58°]
x = 1/2[(360° - 116°) - 116°]
x = 1/2[244° - 116°]
x = 1/2[128°]
x = 64°
The answer is kindly 21 (100% correct)
