Question

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

Answer 1

length of FL will be 1.9318a

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.

`(sinK)/(FL)=(sinL)/(a)`

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

`a* sin105=(\text{FL})* sin30`

FL =
`(a* (sin105))/(sin(30))`

FL =
`a* (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