In the diagram below, a right-angled triangle has a line descending from its right angle, perpendicular to the hypotenuse. If the hypotenuse length is 100cm, and if the line splits the base into 36cm and 64cm parts, what are the side lengths of the original right- angled triangle?

Find the length of a chord that is 3 cm from the center of a circle withradius 7 cm.

2)Kira is participating in a cycle-a-thon to raise money for cancer research. The course that has been set up for participants to travel is in the shape of a triangle. Two of the angles of the course are 113 and 47, and the length of the side between these two angles is 4.1 km. For each kilometre that Kira cycles, she will raise $14.70 for cancer research. Determine how much money Kira raises if she cycles the course 3 times.

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.