Select the correct answer from each drop-down menu. ∆ABC has A (-3, 6), B (2, 1), and C (9, 5) as its vertices. The length of side AB is units. The length of side BC is units. The length of side AC is units. ∠ABC ≈ °.

√50

√65

√145

105 °

√50

√65

√145

105 °

Step-by-step explanation:

Given the coordinates

A (-3, 6)

B (2, 1)

C (9, 5)

To find the length of AB, AC and BC, we will use distance formula

√ ((x2-x1) ² + (y2-y1) ²)

AB:

√ (2+3) ² + (1-6) ²

√5²+5²

√50

BC:

√ (9-2) ² + (5-1) ²

√7² + 4²

√49+16

√65

AC:

√ (9+3) ² + (5-6) ²

√12²+1²

√145

To find ∠ABC

cos (B) = c² + a² - b² / 2ca

= 65 + 50 - 145 / 2 (√65) (√50)

cosB = - 0.26311

B = cos^-1 (-0.26311)

= 105 °