Question

Given: △FKL, FK=a m∠F=45°, m∠L=30° Find: FL

No sins plz

Answer 1

FL = 1.9318a

Explanation:

The above problem can be solved using sin rule. The triangle is drawn in the fig in attachment

using sin rule we can write

`(FK)/(sin30) = (FL)/(sin105) = (KL)/(sin45)`

there we write

`(FK)/(sin30) = (FL)/(sin105)`

out FK= a and value of sin30 and sin 105 we get

`(2a)/(1) = (FL)/(0.9659)`

FL = 1.9318a

therefore the required length FL= 1.9318a

Answer 2

1.9318a

Explanation

Angles in a triangle add up to 180. So angle k is

Angle K = 180 -(45+30) = 180 - 75

= 105°

Now using the sine rule,

FK/sinL = FL/sinK

a/sin30 = FL/sin105

FL =(a × sin 105)/sin30

= 0.9659a/0.5

= 1.9318a