In AGHI, h = 300 inches, G=30° and H=29º. Find the length of i, to the nearest
inch.

Answers

Answer 1

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.


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