Triangles

9000046403

Level: 
B
Consider an isosceles triangle, i.e. the triangle with two sides of equal length. The length of the third side is \(4\, \mathrm{cm}\). One of the interior angles is \(120^{\circ }\). Find the area of this triangle.
\(\frac{4\sqrt{3}} {3} \, \mathrm{cm}^{2}\)
\(4\sqrt{3}\, \mathrm{cm}^{2}\)
\(\frac{8\sqrt{3}} {3} \, \mathrm{cm}^{2}\)

9000150501

Level: 
B
A man of height \(180\, \mathrm{cm}\) casts a \(200\, \mathrm{cm}\) shadow. At the same moment, a tree of an unknown height casts a \(35\, \mathrm{m}\) shadow. Find the height of the tree.
\(\frac{63} {2} \, \mathrm{m}\)
\(\frac{350} {9} \, \mathrm{m}\)
\(\frac{72} {7} \, \mathrm{m}\)
\(\frac{36} {35}\, \mathrm{m}\)