×
Back to all chapters

# Classification of Triangles

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

# Classification of Triangles: Level 3 Challenges

For some value $$d,$$ an isosceles triangle has at least one angle of $$(2d-40)$$ degrees and at least one angle of $$(d+20)$$ degrees.

For each of such triangles, let $$\alpha$$ denote the smallest angle in degrees. Then what is the sum of all possible $$\alpha$$'s?

The sides of a triangle have lengths $$11 , 15 , k$$ where $$k$$ is an integer. For how many value(s) of $$k$$ is the triangle obtuse?

###### This question is a part of JEE Novices.

A triangle has sides of length $$\sin( x), \cos (x)$$ and $$\sqrt{1+\sin (x )\cos( x)}$$, with $$x$$ an acute angle.

Find the largest angle of the triangle in degrees.

A line $$AB$$ of length $$l$$ makes up one side of a triangle. The locus of all points $$P$$ such that $$\triangle ABP$$ is a right triangle with $$\angle P = 90^{\circ}$$ encloses an area of $$\text{__________}$$.

The two larger angles of an isosceles triangle have a combined measure of $$135^\circ$$. If this triangle has a perpendicular height of $$2\text{ m}$$, find the length of its base in meters.

If the latter can be expressed in the form $$a\sqrt { b } -c$$, where $$a,b$$ and $$c$$ are positive integers with $$b$$ square-free, write your answer as $$a\times b\times c$$.

×