Part a) we know that ABC is a right triangle ∠ACB=45° AC=hypotenuse------> 6√2 cm sin 45=AB/AC-----> AB=AC*sin 45----> AB=6√2*√2/2----> AB=6 cm
the answer part a) is AB=6 cm
Part b) we know that volume of the pyramid=(1/3)*Area of the base*height area of the base=50 cm² height=6 cm so volume of the pyramid=(1/3)*50*6----> 100 cm³
In the first three options we can evaluate the values of x with the help of Sine Rule for all the triangles
The Rule says
Where a , b and c are the sides opposite to the angles A, B and C of any ΔABC.
Hence , in order to determine unknown values of sides or angles , we need any 3 values from all 3 sides and 3 angles in a triangle. First Three options give us three values but the last option gives only 2.