Find the length of the hypotenuse of a right-angled triangle using i) Pythagoras Theorem ii) Trigonometry. The triangle has sides of lengths 3cm and 4cm and an acute angle of 30 degrees.

Part iPythagoras Theorem states a² = b² + c² , where a is the hypotenuse.Using this the lengths can be substituted into the equation as b and c, a² = 3² + 4² a² = 25a = sqrt(25) = 5cmPart iiTrigonometric rules allow us to use one angle and one length of a right-angled triangle to calculate the other lengths.Using SOH CAH TOA we can apply sin(angle) = Opposite/HypotenuseTherefore, if the side of length 3cm is opposite to the acute angle of 30 degrees then,Hypotenuse = 3/sin(30)Hypotenuse = 3/0.5Hypotenuse = 6