Question

In ∆HIJ, i=99 inches and < H=9°. Find the length of h, to the nearest inch.

Answer 1

h = 16 in

Step-by-step explanation

We can solve this using the law of sines:

In this case, the relation is:

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

WIth the first two ratios we have:

`(99)/(\sin I)=(99)/(\sin J)`

We can find that angles I and J are equal:

`\begin{gathered} (\sin J)/(\sin I)=(99)/(99) \\ (\sin J)/(\sin I)=1 \\ \sin J=\sin I \\ J=I \end{gathered}`

Therefore, they measures - because the interior angles of a triangle add up 180º- are:

`\begin{gathered} m\angle H+m\angle J+m\angle I=180º \\ 9º+2m\angle J=180º \\ m\angle J=(180º-9º)/(2) \\ m\angle J=m\angle I=85.5º \end{gathered}`

Now, using the law of sines, we can find h:

`\begin{gathered} (i)/(\sin I)=(h)/(\sin H) \\ (99)/(\sin85.5º)=(h)/(\sin 9º) \\ h=99\cdot(\sin 9º)/(\sin 85.5º) \\ h=15.535in \end{gathered}`

Rounded to the nearest inch, h = 16 in