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Geometry

Properties of Triangles

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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