Activities-Pythagoras theorem problems

1. In Right angled ∆ABC,∟BAC= 90°,∟B: ∟C = 1:2 andAC= 4cm.calculate thelenght of BC

'Solution'''' in some special right angled triangle

whose angle ratio 1:2:3 that is 30-60-90

has their sides ratio 1: ${\sqrt {3}}$ :2

in ▲ABC, BC = 2. AC

BC = 2.4

BC = 8 cm

1. A door of width 6 mt has an archabove it having aheight of 2 mt , find the radius if the arch
2. The sides of a right angled triangle are in an AP. Show that sides are in ther ratio 3:4:5