Question

Ray AX is the bisector of angelBAC and ray AY is the bisector of angelXAC. if angleBAY=60° find angelBAC​

Answer 1

To find the angle BAC, we need to use the property that angle bisectors in a triangle divide the opposite side into segments proportional to the other two sides.

Let's call the length of side AC as "a" and the length of side BC as "b". The length of AX can be represented as (a/2)cos(BAC), and the length of AY can be represented as (b/2)cos(BAC).

Since angle BAY = 60°, we can write the following equation using the Law of Cosines:

(a/2)^2 + (b/2)^2 - 2(a/2)(b/2)cos(BAC) = (b/2)^2

Simplifying and solving for cos(BAC), we get:

cos(BAC) = √3/2

Finally, using the inverse cosine function, we can find the value of BAC:

BAC = 60° + 90° = 150°.