Question

in triangle pqr angle q =90 ,angle r=30 and pr=15 find pq
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Answer 1

Answer:

In the given Question:-

In triangle PQR

angle q=90

angle r=30

pr=15

From tables:-

$\sin30 = \frac{1}{2}$

$\cos30 = \frac{ \sqrt{3} }{2}$

By proportion:-

pq:pr=sin 30

pq:15=1/2

Since, product of means=product of extremes

pq=15/2

pq=7.5

In the same way we find qr

qr:pr=cos 30

qr:15=√3/2

Since product of means=product of extremes

2qr=15×√3

qr=7.5√3

Hence,

PQ=7.5cm

QR=7.5√3cm

Also,

Since,

PQ^2+QR^2=PR^2

7.5^2+(7.5√3)^2=15^2

56.25+168.75=225

225=225

Since,

Pythagoras theorem is applied.

Hence,the given solution is correct.

PQ=7.5cm