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,

`(a)/(\sin A)=(b)/(\sin B)=(c)/(\sin C)`

Using Law of sines, we get

`(h)/(\sin H)=(i)/(\sin I)`

`(300)/(\sin 29^\circ)=(i)/(\sin 121^\circ)`

`(300)/(0.4848)=(i)/(0.8572)`

Multiply both sides by 0.8572.

`(300)/(0.4848)* 0.8572=i`

`530.44554=i`

`i\approx 530`

Therefore, the length of i is about 530 inches.