Activities-Pythagoras theorem problems

1. 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. 2 A door of width 6 mt has an archabove it having aheight of 2 mt , find the radius if the arch

Solution

In figure given AB=6 mt width of door CD=2 mt height of arch let OC is radius of arch OD= x mt jion OB, in ∆ODB ∟D= 90º

$OB^{2}=OD^{2}+DB^{2}$

$(x+2)^{2}=3^{2}+x^{2}$

$4+4x+9=9+x^{2}$

4x=9-4

x=${\frac {5}{4}}$

x=1.25

But OC = 2+x

   OC= 2+1.25
   OC= 3.25 mt

radius of arch is 3.25 mt

1. The sides of a right angled triangle are in an AP. Show that sides are in ther ratio 3:4:5