Question

Find the value of x using the Triangle Angle Bisector Theorem

Answer 1

The triangle bisector theorem states if a ray bisects an angle of a triangle, then it divides the opposite side of the triangle into segments that are proportional to the other two sides, therefore:

`(x)/(8.7)=(16.4)/(11.5)`

Solve for x:

Multiply both sides by 8.7:

`\begin{gathered} 8.7\cdot(x)/(8.7)=8.7\cdot(16.4)/(11.5) \\ x\approx12.41 \end{gathered}`

Answer:

x = 12.41