Question

Find the value of 'y' if `sqrt(3)` = 1.723.
Given your answer correct to 2 decimal places.

Answer 1

Construction: Draw BX ⊥ AE
Then, BD = EX = 14 cm and BX = ED
AX = AE - EX = 16 - 14 = 2

In right ΔAEF,

tan30° = `"FE"/"AE"`

⇒ `(1)/sqrt(3) = "FE"/(16)`

⇒ FE = `(16)/sqrt(3)`
In right ΔBDC,

tan60° = `"BD"/"DC"`

⇒ `sqrt(3) = (14)/"DC"`

⇒ DC = `(14)/sqrt(3)`
In right ΔAXB,

tan45° = `"BX"/"AX"`

⇒ 1 = `"BX"/(2)`
⇒ BX = 2
⇒ ED = BX = 2
Now,
y = FC
FE + ED + DC

= `(16)/sqrt(3) + (14)/sqrt(3) + 2`

= `(30 + 2sqrt(3))/sqrt(3)`

= `(30 + 3.464)/(1.732)`
= 19.32.