Question

In a right triangle ΔABC, the length of leg AC = 5 ft and the hypotenuse AB = 13 ft. Find: The length of the angle bisector of angle ∠A.

PLZ HELP!!

Answer 1

check the picture below.


`\bf cos(\theta)=\cfrac{adjacent}{hypotenuse}\quad cos(CAB)=\cfrac{5}{13}\implies \measuredangle CAB=cos^(-1)\left( (5)/(13) \right) \\\\\\ \textit{that means that }\measuredangle hAC=\cfrac{cos^(-1)\left( (5)/(13) \right)}{2}\impliedby \textit{one of the halves}`

now, notice, for the angle hAC, the hypotenuse is hA, and the adjacent side is CA, therefore,


`\bf cos(\theta)=\cfrac{adjacent}{hypotenuse}\qquad cos(hAC)=\cfrac{5}{hA}\implies hA=\cfrac{5}{cos(hAC)} \\\\\\ hA=\cfrac{5}{cos\left[ (cos^(-1)\left( (5)/(13) \right))/(2) \right]}`

make sure your calculator is in Degree mode, if you need the angle in degrees.