Question

In the given figure, ∠B = 60°, AB = 16 cm and BC = 23 cm,
Calculate:

1. BE
2. AC

Answer 1

In ΔABE,

sin 60° = `"AE"/"AB"`

⇒ `sqrt(3)/(2) = "AE"/(16)`

⇒  AE = `sqrt(3)/(2) xx 16`

= `8sqrt(3)  "cm"`

(i) In ∆ABE,

m∠AEB = 90°

∴ By Pythagoras Theorem, we get
BE² = AB² - AE²
⇒ BE² = (16)² - (8√3)²
⇒ BE² = 256 - 192
⇒ BE² = 64
⇒ BE = 8 cm

(ii) EC = BC - BE = 23 - 8 = 15
In ∆AEC, 
m∠AEC = 90°

∴ By Pythagoras Theorem, we get
AC² = AE² + EC²
⇒ AC² = (8√3)² + (15)²
⇒ AC² = 192 + 225
⇒ AC² = 417
⇒ AC = 20. 42 cm