Question

Multiple choiceA. 2.14 unitsB. 3.3 unitsc. 6.4 unitsD. 7.1 units

Answer 1

the approximate length of GH is;

`GH=6.4\text{ units}`

Step-by-step explanation:

Given the figure in the attached image;

The adjacent side and the acute angle of the triangle are given as;

`\begin{gathered} \text{Adjacent =3} \\ \text{Acute angle = 65}^(\circ) \end{gathered}`

We want to find the length of the side opposite the Acute angle.

From the given table, for angle 65 degree, the ratio of the opposite side to the adjacent length is;

`\frac{\text{opposite leg length}}{\text{adjacent leg length}}=2.14`

Let x represent the opposite leg length GH.

substituting the values;

`\begin{gathered} \frac{\text{opposite leg length}}{\text{adjacent leg length}}=2.14 \\ (x)/(3)=2.14 \\ x=3*2.14 \\ x=6.42 \\ x=6.4\text{ units} \end{gathered}`

Therefore, the approximate length of GH is;

`GH=6.4\text{ units}`