please show work 6 Solve the following triangle SolutionThe

please show work.

Solution

The image is not very clear despite zooming, so pardon me please if I assume certain figures which may turn out to be incorrect.

When we know 2 sides of a triangle and an angle which is not between these 2 sides, we use the following property of the triangle to find the 3rd side:

Sin (A)/a = Sin(B)/b + Sin (C)/c.

In the image given to us, one side ( say a) appears to be of 4.92 inches and the angle (A) opposite it appears to be of 72 degrees. Anotherside (say b) appears to be of 1.85 inches. We have to find the 3rd side (say c) and the other two angles B and C. Using the above property of a triangle, we have Sin (72)/ 4.92 = Sin (B)/ 1.85. Therefore, Sin (B) = (1.85/4.92)(Sin 72) = 1.85*0.9511/4.92 = 0.3576 . Therefore B = Sin^-1 ( 0.3576) = 20.95 degrees. Since the sum of three angles A , B , C of a triangle is 180 degrees, the 3rd angle C = 180 - 72 - 21.95 = 86.05 degrees.

Now, in order to find the 3rd side c, we have Sin (A) /a = Sin (C) /c or, Sin (72)/ 4.92 = Sin (86.05)/c. Therefore, c = [Sin(86.05)/Sin (72)]*4.92 = (0.9976//0.9511)*4.92 =( 1.04896)* 4.92 = 5.16 inches.

If the figures used are incorrect, please use the above methodology with correct figures to get the result.