Question

In triangle PQR, right angle is at Q . If PQ= 3cm and PR= 6cm, find angle QPR and angle PRQ​

Answer 1

ɢɪᴠᴇɴ ᴛʜᴀᴛ :<ϙ=90,

ᴘϙ=3

ᴘʀ=6

ɴᴏᴡ ʙʏ ᴀᴘᴘʟʏɪɴɢ sɪɴᴇ ʀᴜʟᴇ :

sɪɴʀ/ᴘϙ=sɪɴϙ/ᴘʀ

ʙʏ ᴘᴜᴛᴛɪɴɢ ᴠᴀʟᴜᴇs ғʀᴏᴍ ᴛʜᴇ ϙᴜᴇsᴛɪᴏɴ ᴡᴇ ɢᴇᴛ

sɪɴʀ/3=sɪɴ90/6

ᴏɴ sᴏʟᴠɪɴɢ

sɪɴʀ=1/2

<ʀ=30

ʙʏ ᴀᴘᴘʟʏɪɴɢ ᴘʀᴏᴘᴇʀᴛʏ ᴏғ ʀɪɢʜᴛ ᴀɴɢʟᴇ

<ᴘ+<ϙ+<ʀ=180

<ᴘ+90+30=180

<ᴘ=180–120

<ᴘ=60

sᴏ ᴀɴsᴡᴇʀ ɪs <ᴘ $ <ʀ ɪs 60 $30

Answer 2

Given: PQ = 3cm

PR = 6cm

$Therefore,\frac{PQ}{PR} = sin R \\ \\ </p><p>sin R = \frac{3}{6} = \frac{1}{2} \\ \\ \angle {PRQ}=30°</p><p>\\ \\ \angle{QPR} = 60°$