Question

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

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

$m\angle G+m\angle H+m\angle I=180^\circ$

$30^\circ+29^\circ+m\angle I=180^\circ$

$59^\circ+m\angle I=180^\circ$

$m\angle I=180^\circ-59^\circ$

$m\angle I=121^\circ$

According to Law of sines,

$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$

Using Law of sines, we get

$\dfrac{h}{\sin H}=\dfrac{i}{\sin I}$

$\dfrac{300}{\sin 29^\circ}=\dfrac{i}{\sin 121^\circ}$

$\dfrac{300}{0.4848}=\dfrac{i}{0.8572}$

Multiply both sides by 0.8572.

$\dfrac{300}{0.4848}\times 0.8572=i$

$530.44554=i$

$i\approx 530$

Therefore, the length of i is about 530 inches.