Given:
In triangle GHI, h = 300 inches, G=30° and H=29º.
To find:
The length of i.
Solution:
We have, G=30° and H=29º.
Using angle sum property, we get
[tex]m\angle G+m\angle H+m\angle I=180^\circ[/tex]
[tex]30^\circ+29^\circ+m\angle I=180^\circ[/tex]
[tex]59^\circ+m\angle I=180^\circ[/tex]
[tex]m\angle I=180^\circ-59^\circ[/tex]
[tex]m\angle I=121^\circ[/tex]
According to Law of sines,
[tex]\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
Using Law of sines, we get
[tex]\dfrac{h}{\sin H}=\dfrac{i}{\sin I}[/tex]
[tex]\dfrac{300}{\sin 29^\circ}=\dfrac{i}{\sin 121^\circ}[/tex]
[tex]\dfrac{300}{0.4848}=\dfrac{i}{0.8572}[/tex]
Multiply both sides by 0.8572.
[tex]\dfrac{300}{0.4848}\times 0.8572=i[/tex]
[tex]530.44554=i[/tex]
[tex]i\approx 530[/tex]
Therefore, the length of i is about 530 inches.
