Classification of Triangles: Level 3 Challenges Practice Problems Online

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?

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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 $a\times b\times c$ .

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Classification of Triangles: Level 3 Challenges

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Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 7 million people

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Classification of Triangles

Concept Quizzes

Challenge Quizzes

Classification of Triangles: Level 3 Challenges

This question is a part of JEE Novices.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.