In triangle XYZ, XZ=6, ZX=7, and XY=8, find (sinY+sinZ)/sinX.

Answer 1

Typo? XZ=6 and ZX=7 ?? , I will assume you meant YZ=7

Use the area of the triangle formula in terms of the sine of the contained angle.

Area = A = (1/2)(7)(8)sinY ---> sinY = A/28
Also A = (1/2)(6)(7)sinZ ----> sinZ = A/21
and A = (1/2)(6)(8)sinX -----> sinX = A/24

(sinY + sinZ)/sinX
= (A/28 + A/21)/(A/24) , divide top and bottom by A
= (1/28 + 1/21)/(1/24)
= (1/12)(24/1)
= 2