Question

In ΔАBC, AB = AC = 15 cm, BC = 18 cm, find cos ∠ABC.

Answer 1

Given: In triangle ABC: AB = AC = 15 cm, BC = 18 cm.

Step-wise calculation:

1. Use the law of cosines at angle B:

AC² = AB² + BC² – 2 × AB × BC × cos∠ABC

2. Solve for cos ∠ABC: 

`cos∠ABC = (AB^2 + BC^2 - AC^2)/(2 xx AB xx BC)` 

= `(15^2 + 18^2 - 15^2)/(2 xx 15 xx 18)` 

= `18^2/(2 xx 15 xx 18)` 

= `18/(2 xx 15)` 

= `324/540` 

= `3/5`