Question

If CL is a bisector, how do i solve this?

Answer 1

Explanation:

First equation: Use angle bisector theorem

`(x)/(y)` =
`(35)/(21)` ,
`(x)/(y)` =
`(5)/(3)` ⇒ x =
`(5)/(3)` y ............ (1)

Second equation: Use cosine law

x² + y² - 2xycos 120° = ( 35 + 21 )² , cos 120° = - 0.5

x² + y² + xy = 56² ................. (2)

(1) ----> (2)

(
`(5)/(3)` y )² + y² +
`(5)/(3)` y² = 56² ............. (3)

9 × (3)

25y² + 9y² + 15y² =( 9 ) × 56²

7²y² = (168)²

y = 24

x =
`(5)/(3)` × 24 = 40

AC = 40

BC = 24

m∠A ≈ 22 ° ( see the attachment )

m∠B ≈ 38 °