[b]Assignment.[/b] Determine [math]x[/math], and calculate the area of the triangle below.

[b]Solution.[/b] The hypotenuse [math]x[/math] can be obtained by using sine:[br][br][math] \large \begin{array}{rcll}[br]\sin(61,2^{\circ}) & = & \frac{14,2 \, \mathrm{m}}{x} & | \cdot x \\[br]x \cdot \sin(61,2^{\circ}) & = & 14,2 \, \mathrm{m} & | : \sin(61,2^{\circ}) \\[br]x & = & \frac{14,2 \, \mathrm{m}}{\sin(61,2^{\circ})} = 16,204 \ \mathrm{m}[br]\end{array} [/math][br][br]To obtain the missing leg (let us denote it [math]a[/math]), we use Pythagoras' theorem. For simplicity, we drop the measurement units in the equation:[br][br][math] \large \begin{array}{rcll}[br]14,2^2 + a^2 & = & 16,204^2 \\[br]a^2 & = & 16,204^2 - 14,2^2 \\[br]a^2 & = & 60,942 \\[br]a & = & \sqrt{60,94} = 7,807 \, (\mathrm{m}) [br]\end{array} [/math][br][br]Finally, we calculate the area of the triangle:[br][br][math] \large A = \frac{1}{2} \cdot 14,2 \, \mathrm{m} \cdot 7,807 \, \mathrm{m} = 55,426 \, \mathrm{m^2} . [/math][br][br][b]Answers:[/b] the hypotenuse [math]x[/math] is [math]16,2 \, \mathrm{m}[/math], and the area of the triangle is [math]55,4 \, \mathrm{m^2}[/math].