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Classification of Triangles

Can a scalene triangle be obtuse? Is an equilateral triangle always acute?

Level 2

         

Two sides of a triangle measures \(10\text{ cm}\) and \(6\text{ cm}\) and the angle in between them measures \(120^\circ\). What is the measure of the third side (in \(\text{cm}\))?

A triangle has a \(60^\circ\) angle. If two of its sides are \(1\text{ m}\) long, how many different triangles can one draw which fit these measurements?

A square and an equilateral triangle have the same perimeter. If the area of the triangle is \(16 \sqrt{3}\), what is the area of the square?

If the sides of a non-degenerate triangle are \(a,b,\sqrt{a^2+b^2+ab} \), then find the measure of the greatest interior angle of this triangle (in degrees).

The length of two sides of an isosceles triangle are 5 units and 16 units. What is the perimeter of the triangle (in units)?

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