Two right-angled triangles are described as follows: • ( PQR ) is right-angled at (Q…

MATHEMATICS · Multi-part · CBSE · Mathematics · Triangles · Triangles

Problem

Two right-angled triangles are described as follows: •

\triangle PQR

is right-angled at

Q

with

PQ = 8\,\text{cm}

and

QR = 15\,\text{cm}.

•

\triangle STU

is right-angled at

T

with

ST = 16\,\text{cm}

and

TU = 30\,\text{cm}.

(i) Find the lengths of the hypotenuses

PR

and

SU

. (ii) Calculate

\sin P

and

\sin S

. (iii) Compare the values obtained in part (ii) and deduce the relationship between angles

P

and

S

. (iv) Using your deduction, state with reason whether

\triangle PQR

and

\triangle STU

are similar.