Solve the following triangle, rounding answers to the nearest tenth if necessary. In ∆𝐸𝐹𝐺, ∠𝐹 = 67.8°, 𝑓 = 12.5 𝑚, 𝑎𝑛𝑑 𝑒 = 9.8 m

Question

This is a right triangle, I believe.

Answer 1

use the law of sines: sinF/f = sinE/e = sinG/g

sin67.8/12.5 = sinE/9.8

sinE = 9.8sin67.8/12.5

E=41.8

G= 180-41.8-67.8 = 180-109.6 = 70.4 degrees

g/sinG = 9.8/sinE

g/sin70.4 = 9.8/2/3= 3/2(9.8= 14.7

g= 14.7(sin70.4) = 13.85

sides of the triangle are e,f and g = 9.8, 12.5 and 13.85 or 13.9

angles are E, F and G = 41.8, 67.8 and 70.4 degrees

It's a right triangle only if one angle = 90 degrees