A right angled triangle has 2 known sides measuring 3 meters, 4 meters respectively. Find the hypotenuse and the smallest angle in the triangle.

This is an example of a pythagoras. The student has to use the knowledge that the hypotenuse (longest side) is the square root of the sum of the squares of the known sides. In this instance, it would be 4^2 + 3^2 = 16 + 9 = 25 the square root of 25 is 5 and therefore the missing length is 5 meters.  The smallest angle in the triangle can be seen by using a diagram and finding that the angle would be between the 5 meter length side and the 4 meter length side. The angle can be determined by using the SohCahToa analogy. As we have now worked out all of the sides of the triangle, we can use either sin, cos or tan. In this instance, i am using sine to work out the angle. This concerns the hypotenuse and opposite sides (to the angle in question) Sin (x) = 3/5. By using the inverse we find that x and hence the smallest angle is 36.8 degrees.