Given: △FKL, FK=a
m∠F=45°, m∠L=30°
Find: FL
2 answers:
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.
FL =
FL =
= 1.9318a
Therefore, length of FL will be 1.9318a
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
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