# Difference between revisions of "Activities-Pythagoras theorem problems"

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

''''''Solution''''''''' | ''''''Solution''''''''' | ||

in some special right angled triangle | in some special right angled triangle | ||

Line 12: | Line 12: | ||

BC = 8 cm | BC = 8 cm | ||

− | #A door of width 6 mt has an archabove it having aheight of 2 mt , find the radius if the arch | + | #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 | ||

+ | |||

+ | <math>OB^2=OD^2+DB^2</math> | ||

+ | |||

+ | <math>(x+2)^2=3^2+x^2</math> | ||

+ | |||

+ | <math>4+4x+9=9+x^2</math> | ||

+ | |||

+ | 4x=9-4 | ||

+ | |||

+ | x=<math>\frac{5}{4}</math> | ||

+ | |||

+ | x=1.25 | ||

+ | |||

+ | But OC = 2+x | ||

+ | |||

+ | OC= 2+1.25 | ||

+ | OC= 3.25 mt | ||

+ | radius of arch is 3.25 mt | ||

+ | |||

+ | |||

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

## Revision as of 07:09, 11 July 2014

- 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: :2

in ▲ABC, BC = 2. AC

BC = 2.4

BC = 8 cm

- 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

4x=9-4

x=

x=1.25

But OC = 2+x

OC= 2+1.25 OC= 3.25 mt

radius of arch is 3.25 mt

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