Triangle GHI has i= 19 m, H=137 degrees, and I=51degrees. Find g.
Happy Thanksgiving.
angle G = 180-137-51 = 8°
so now by the Sine Law
g/sin8 = 19/sin51
g = 19sin8/sin51 = appr. 3.4
To find the length of side g in triangle GHI, we can use the Law of Sines. The Law of Sines states that the ratio of the length of each side of a triangle to the sine of its opposite angle is constant.
In this case, we can use the relationship between side i, angle H, and side g:
sin(137 degrees) / g = sin(51 degrees) / (19 m)
To solve for g, we need to rearrange the equation:
g = (sin(137 degrees) * 19 m) / sin(51 degrees)
Now we can calculate the value of g:
g = (sin(137 degrees) * 19 m) / sin(51 degrees)
Using a scientific calculator, we can evaluate the sine of 137 degrees and 51 degrees, and then calculate g.