Rectangle

Calculate the length of the side GN and diagonal QN of rectangle QGNH when given: |HN| = 25 cm and angle ∠ QGH = 28 degrees.

Correct answer:

|GN| =  13.29 cm
|QN| =  28.31 cm

Step-by-step explanation:

$$\begin{gathered} \alpha =28^{\circ } \\ a=\mathrm{\mid }HN\mathrm{\mid }=25cm \\ \tan \alpha ={\displaystyle \frac{b}{a}} \\ b=\mathrm{\mid }GN\mathrm{\mid }=a\tan \alpha =13.29\text{ cm} \end{gathered}$$

$$\begin{gathered} \cos \alpha ={\displaystyle \frac{a}{u}} \\ u=\mathrm{\mid }QN\mathrm{\mid }={\displaystyle \frac{a}{\cos \alpha }}=28.31\text{ cm} \end{gathered}$$

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