Answer:
length of FL will be 1.9318a
Step-by-step explanation:
Given : In triangle FKL,
FK = a
m∠F = 45° and m∠L = 30°
To Find : Measure of FL.
Since sum of all angles of a triangle equals to 180°.
m∠F + m∠L + m∠K = 180°
45 + 30 + m∠K = 180°
m∠K + 75° = 180°
m∠K = 180 - 75
m∠K = 105°
Now we apply sine rule in the given triangle.
[tex]\frac{sinK}{FL}=\frac{sinL}{a}[/tex]
[tex]\frac{sin105}{FL}=\frac{sin30}{a}[/tex]
[tex]a\times sin105=(\text{FL})\times sin30[/tex]
FL = [tex]\frac{a\times (sin105)}{sin(30)}[/tex]
FL = [tex]a\times \frac{0.966}{0.5}[/tex]
= 1.9318a
Therefore, length of FL will be 1.9318a
