Question

a triangle has side cequals6 and angles equals startfraction pi over 4 endfraction and equals startfraction pi over 3 endfraction . find the length a of the side opposite a. the length of side a is nothing.

Answer 1

Answer:

$a=\frac{12}{1+\sqrt{3}}$

Step-by-step explanation:

c=6

Angle A= π/4

Angle B= π/3

Angle C = π - (π/4+π/3)= 5π/12

We want to determine side A.

Using Sine Rule

$\frac{a}{Sin A}=\frac{c}{Sin C}$

$\frac{a}{Sin \frac{\pi}{4}}=\frac{6}{Sin \frac{5\pi}{12} }$

$a=\frac{6}{Sin \frac{5\pi}{12} } X Sin \frac{\pi}{4}$

$a=\frac{12}{1+\sqrt{3}}$

a=4.39