Question

A man of height 156 cm stands under a semicircular arc at a distance of 36 cm
from one end such that his head touches the arc. Find the width of arc.​

Answer 1

Answer:

Step-by-step explanation:

Width= 712 cm

Answer 2

A man of height 156 cm standing under a semicircular arc at a distance of 36 cm from one and such that his head touches the arc. The width of arc is 712 cm. Step wise explanation is given below :

- As it is told that ΔACD ,ΔBCD because CD is a perpendicular AB and ΔABD is a right angle triangle.

- So, by using pythagoras theorem

In ΔACD

Y^2=(156)^2+(36)^2. ...(1)

InΔBCD

Z^2=(156)^2+(x)^2. ...(2)

- In ΔABD

(36+x)^2=(Y)^2+(Z)^2

- From (1) and (2)

(36+x)^2=[(156)^2+(36)^2]+[(156)^2+(x)^2]

(x)^2+72x+1296=(156)^2+(36)^2+(156)^2+(x)^2

72x=24336+ 1296+ 24336 +(x)^2-(x)^2 -1296

72x= 48672

x= 48672/72

x=676. ...(3)

- So,the width of the arc is

AB=AC+BC

AB= 36+ 676. ...[from(3)]

AB= 712cm

- Hence, the width of arc is 712cm.