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

[TeX]a=\frac{12}{1+\sqrt{3}}[/Tex]

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

[TeX]\frac{a}{Sin A}=\frac{c}{Sin C}[/Tex]

[TeX]\frac{a}{Sin \frac{\pi}{4}}=\frac{6}{Sin \frac{5\pi}{12} }[/Tex]

[TeX]a=\frac{6}{Sin \frac{5\pi}{12} } X Sin \frac{\pi}{4}[/Tex]

[TeX]a=\frac{12}{1+\sqrt{3}}[/Tex]

a=4.39