The great pyramid of Giza has a square base of side 230m. One of the sloping edges makes an angle of 42° with the base. Find the height of the pyramid.

A tree casts a shadow 14 feet long. A flagpole that is 20 feet tall casts a shadow 8 feet long. The triangle formed by the tree and its shadow is similar to the triangle formed by the flagpole and its shadow. Verify that the tree is 35 feet tall.

Find the remaining sides of a 30°–60°–90° triangle if the longest side is 9.

A tree has snapped part of the way up it’s trunk and has fallen onto the ground, making a 300 angle with the ground at its tip. If the portion of the tree which has broken and contacted the ground is 10 metres long, how far is the top of the tree from the base still standing? Draw a diagram and express your answer in simplest radical form.