Question

Using a compass and straightedge only, do the following:

a.) Construct the figure

b.) Write out step by step how to construct the figure

1.) Using a compass and straightedge only, construct a segment that is of length $3^(1/4)$. Note, a segment of length 1 is given below and must be used.

Answer 1

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To Construct 4 squareroot 3 consider a right angled triangle whose base and perpendicular are our unit lengths 1 By Pythagorean theorem H^2 = 1^2 + 1^2 Rightarrow H = squareroot 2 Thus we have constructed a line of length squareroot 2 Now from this line, we construct another right angled triangle whose base is H = squareroot 2 & perpendicular 1 Again By Pythagorean Theorem H'^2 = squareroot^2 + 1^2 Rightarrow H' = squareroot 3 This AB = squareroot 3 be the line segment, place the unit length on the line where the line AB starts, starting a point A and in the direction opposite to B: Let C be another point of the segment. Now draw a Semicircle with diameter BC and a perpendicular to A: This line touches the semicircle at a point O. Clearly triangle BCD is right angles at D lik the triangle ACD two angles of