Loading [MathJax]/jax/output/SVG/jax.js
 
+0  
 
0
3
1
avatar+936 

In triangle ABC, AB=3, AC=5, BC=7, and D lies on ¯BC such that ¯AD bisects BAC. Find cosBAD.

 Jan 30, 2025
 #1
avatar+130383 
+1

Law of Cosines

 

BC^2  = AC^2 + AB^2  - 2 (AC * AB) cos (BAC)

 

7^2  = 5^2 + 3^2 - 2 ( 5 * 3) cos (BAC)

 

[ 7^2 -5^2 -3^2] / [ -2 * 5 * 3] =  cos (BAC)   =  -1/2

 

arccos (-1/2)  =  BAC =   120°

 

Since AD is a bisector ofthis angle, then BAD  = 60°

 

cos 60°  = cos (BAD)  =  1/2

 

 

cool cool cool

 Jan 30, 2025

1 Online Users