Question

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

Answer 1

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.

$\frac{sinK}{FL}=\frac{sinL}{a}$

$\frac{sin105}{FL}=\frac{sin30}{a}$

$a\times sin105=(\text{FL})\times sin30$

FL = $\frac{a\times (sin105)}{sin(30)}$

FL = $a\times \frac{0.966}{0.5}$

    = 1.9318a

Therefore, length of FL will be 1.9318a

Answer 2

The sum of angles in a triangle is 180°, so the measure of ∠K is ...

... 180° - 45° - 30° = 105°

Then the Law of Sines tells you ...

... FL = FK/sin(L)×sin(K)

... FL = sin(105°)/sin(30°)×a ≈ 1.93185a