A decorative gateway is shaped as a semicircular arch whose straight base is long

MATHEMATICS · Multi-part · CBSE · Mathematics · The Baudhayana-Pythagoras Theorem · The Baudhayana-Pythagoras Theorem

Problem

A decorative gateway is shaped as a semicircular arch whose straight base

PQ

20\,\text{m}

long. A light is to be mounted at a point

R

on the curved edge such that the distance from

P

R

13\,\text{m}

. (i) Prove that

\triangle PRQ

is a right-angled triangle. (ii) Calculate the length

QR

. (iii) The height of the arch at

R

is the perpendicular distance from

R

to the base

PQ

. Determine this height correct to one decimal place.