use a ruler and a pair of compasses only construct a triangle ABC given that AB=5cm, angle BAC=75 degrees and angle ABC=60 degrees .construct and measure the perpendicular from B to the side AC.
To construct triangle ABC, we first draw line AB of length 5 cm using the ruler. Then, using the compass, we draw an arc with radius 5 cm centered at A. We then draw another arc with radius x cm centered at B, where x is some arbitrary length. The two arcs should intersect at a point, which we label as C.
Next, we use the compass to draw an arc with radius AB centered at A, and another arc with radius BC centered at B. The two arcs should intersect at a point, which we label as D. We then draw a line through D and C to complete the triangle ABC.
To measure the perpendicular from B to the side AC, we first draw a line through B parallel to AC, using the ruler. We then draw a line through D perpendicular to this line, extending it to intersect with the line AC at a point, which we label as E. The line BD is then the perpendicular from B to the side AC.
To measure the length of BD, we use the ruler to measure the distance from B to E, which is the same as the length of BD.