Let alpha pi6 b 10 a 5 be given Choose the most correct a

Let alpha = pi/6, b = 10, a = 5, be given. Choose the most correct answer regarding the existence of such a triangle w measurements. No such triangle exists. Only one such triangle exists. Only one such triangle exists and it is a right triangle. Exactly two such triangles exist. There are more than two such triangles. Rewrite as an algebraic expression: cos (arccosx - arctan x) Find the general solution of cos 2 alpha + cos 4 alpha = 0. A Tethered Aerostat Radar System (TARS) is a low-level airborne j lance system that uses aerostats (moored balloons) as radar platforms. Suppo maintains an altitude of 5200 m and the tether is pulled taut at an angle of 57 degree Find the exact length of the tether.

Solution

6. alpha=pi/6, a=5, b=10

Using sine law

sin alpha/a= sin beta/b

sin 30/ 5= sin beta/10

sin beta= 10 sin 30/5= 1

beta=pi/2= 90 degree

gamma= 180 - alpha - beta= 60 degree

sin gamma/c= sin alpha/a

sin 60/c= sin 30/5

c= 5 sin 60/ sin 30= 8.66

one such triangle possible