Question

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

Answer 1

Answer:

The length of the angle bisector of angle ∠A is 6.01.

Step-by-step explanation:

It is given that length of leg AC = 5 ft and the hypotenuse AB = 13 ft.

Using pythagoras theorem

$(AB)^2=(BC)^2+(AC)^2$

$(13)^2=(BC)^2+(5)^2$

$169=(BC)^2+25$

$BC=12$

$\sin A=\frac{\text{perpendicular}}{\text{hypotenuse}}$

$\sin A=\frac{BC}{AB}$

$A=\sin ^{-1}\frac{12}{13}$

$A=67.38$

Bisector divides the angle in two equal parts, therefore,

$A'=\frac{67.38}{2} =33.69$

In triangle ACD.

$\cos A'=\frac{\text{Base}}{\text{Hypotenuse}}$

$\cos A'=\frac{AC}{AD}$

$\cos (33.69^{\circ})=\frac{5}{AD}$

$0.832=\frac{5}{AD}$

$AD=\frac{5}{0.832} =6.009\approx 6.01$

Therefore the length of the angle bisector of angle ∠A is 6.01.