Question

In the given figure,Angle A is bisected by AD. Angle BAC=80⁰.What is the value of Angle BAD in degrees.​

Answer 1

Step-by-step explanation:

△ABC,AD is the angle bisector of ∠BAC,AB=4 cm, and AC=3 cm, as given in the figure below.

By the property of the angle bisector, we have, BDDC=ABAC=43.

Let BD=4x,DC=3x and AD=y.

By the cosine rule, we have, cos(∠BAC)=AB2+AC2−BC22⋅AB⋅AC.

⇒cos60o=16+9−49x224⇒12=25−49x224.

⇒x=13√7.

⇒BD=413√7 and DC=313√7.

By the cosine rule, we have, cos(∠BAD)=AB2+AD2−BD22⋅AB⋅AD.

⇒cos30o=16+y2−208498y=3√2.

⇒y2=43–√y−16+20849.

By the cosine rule, we have, cos(∠DAC)=AD2+AC2−DC22⋅AD⋅AC.

⇒cos30o=9+y2−117496y=3√2.

⇒y2=33–√y−9+11749.

⇒43–√y−16+20849=33–√y−9+11749.

⇒3–√y=16−20849−9+11749=7−9149=367.

⇒y=3673√=123√7.

⇒AD=123√7.