A right-angled triangle has three sides that are in proportion. The three sides are the opposite, the adjacent and the hypotenuse. The approximate length of side GH is 6.4 units.
The given ratios are:
[tex]\left[\begin{array}{cccc}{Angles}&55^o&65^o&75^o\\\frac{Adjacent}{Hypotenuse}&0.57&0.42&0.26\\ \frac{Opposite}{Hypotenuse}&0.82&0.91&0.97\\ \frac{Opposite}{Adjacent}&1.43&2.14&3.73\end{array}\right[/tex]
See attachment for triangle
To calculate length GH, we use the following trigonometry ratio:
[tex]\tan(\theta) = \frac{Opposite}{Adjacent}[/tex]
Rewrite as:
[tex]\tan(65) = \frac{GH}{HI}[/tex] and [tex]\tan(65) = \frac{Opposite}{Adjacent}[/tex]
From the given table, the value of tan(65) is 2.14:
[tex]\tan(65) = 2.14[/tex]
Substitute [tex]\tan(65) = 2.14[/tex] in [tex]\tan(65) = \frac{GH}{HI}[/tex]
[tex]2.14 = \frac{GH}{HI}[/tex]
Make GH the subject
[tex]GH = 2.14 \times HI[/tex]
Substitute 3 for HI
[tex]GH = 2.14 \times 3[/tex]
[tex]GH = 6.42[/tex]
Approximate
[tex]GH = 6.4[/tex] --- to 1 decimal place
Hence, the approximated length of GH is 6.4 units
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