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Properties of Triangles

Given a triangle with side lengths of 5, 12, and 14, is the largest angle in the triangle acute, right, or obtuse? Geometric knowledge helps us deduce much about triangles from limited information.

Properties of Triangles: Level 2 Challenges


A vertical pole AB measuring 5 meters snaps at point C. The pole remains in contact at C and the top of the pole touches the ground at point T, a distance of 3 meters from A.
Find the length AC, in meters, the point where the pole snapped.

Let \(ABC\) be a triangle with \(\angle B=90^\circ\), \(\angle C=30^\circ\) and \(AB=5\) Find the length of the angle bisector from \(A\) to \(\overline{BC}\)(right to \(2\) decimal places).

Figure above shows an isosceles right triangle \(ABC\) with \(AB = AC = 6 \). Given that \(SDPF\) is a square, find the area of the square \(SDPF\).

The two red lines in the diagram shown are drawn diagonally on the faces of a cube. What is the angle (in degrees) between them at the point where they join?

In the image above, \(\overline { ZW } \bot \overline { XY },\) \(\overline { XW } =16\) and \(\overline { WY } =9\). Find \(\overline { ZY } +\overline {XY } \)


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