Question

A man of height 156 cm stands under a semi-circular arc at a distance of 36cm from one end such that it touches the arc. Find the width of arc.

Answer 1

Step-by-step explanation:

Given A man of height 156 cm stands under a semi-circular arc at a distance of 36 cm from one end such that it touches the arc. Find the width of arc.

• Given a man  whose height is 156 cm is standing under a semi circular arc and the distance is 36 cm. We need to find the width of arc.
• Applying Pythagoras theorem we get ( r – 36 is base , height is 156 cm and we need to find opposite side r)
• So r^2 = 156^2 + (r – 36)^2
• So r^2 = 156^2 + r^2 + 36^2 – 2 (36) r
• So r^2 = 156^2 + r^2 + 36^2 – 72 r
• So 72 r = 156^2 + 36^2
•       72 r = 25,632
• Or r = 25,632 / 72
• Or r = 356 cm
• We know that diameter d = 2 r
•    Or d = 2 x 356
•  Or d = 712 cm

Reference link will be

https://brainly.in/question/15895430