Question

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

Answer 1

Answer:

FL=b

sin K/b=sin L/a

b=( sin K *a)/sinL

Answer 2

Answer:

The value of FL would be 0.9823 a

Step-by-step explanation:

Given,

In triangle FKL,

FK=a, m∠F=45°, m∠L=30°

Since sum of measures of all interior angles of a triangle is 180°,

i.e. m∠F + m∠K + m∠L = 180°

⇒ 45° + m∠K + 30° = 180°

⇒ m∠K + 75° = 180°

⇒ m∠K  = 180° - 75° = 105°,

Using law of sine,

$\frac{\sin L}{FK}=\frac{\sin K}{FL}$

$\frac{\sin 30^{\circ}}{a}=\frac{\sin 105^{\circ}}{FL}$

$FL=\frac{a\sin 105^{\circ}}{\sin 30^{\circ}}\approx 0.9823a$

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