Question

In the given figure, ∠B = 60°, ∠C = 30°, AB = 8 cm and BC = 24 cm. Find:
a. BE
b. AC

Answer 1

a. In right ΔAEB,

sin60° = `"AE"/"AB"`

⇒ `sqrt(3)/(2) = "AE"/(8)`
⇒ AE = `4sqrt(3)"cm"`
Now,
BE² 
= AB² - AE²
= `8^2 - (4sqrt(3))^2`
= 64 - 48
= 16
⇒ BE = 4cm
b. EC
= BC - BE
= 24 - 4
= 20cm
Now,
In right ΔAEC,
AC²
= AE² + EC²
= `(4sqrt(3))^2 + 20^2`
= 48 + 400
= 448
⇒ AC = `8sqrt(7)"cm"`.