Question

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◆ ɪɴ ∆ᴏᴘQ, ʀɪɢʜᴛ ᴀɴɢʟᴇᴅ ᴀᴛ ᴘ, ᴏᴘ = 7ᴄᴍ ᴀɴᴅ ᴏQ -ᴏᴘ = 1ᴄᴍ. ᴅᴇᴛᴇʀᴍɪɴᴇ ᴠᴀʟᴜᴇꜱ ᴏꜰ ᴀʟʟ ᴛʀɪɢᴏɴᴏᴍᴇᴛʀʏ ʀᴀᴛɪᴏꜱ ɪɴ ᴛᴇʀᴍꜱ ᴏꜰ ᴀɴɢʟᴇ Q.


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Answer 1

Answer:

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In Δ OPQ, we have 

OQ2=OP2+PQ2

⇒(PQ+1)2=OP2+PQ2[∵OQ−PQ=1⇒OQ=1+PQ]

⇒PQ2+2PQ+1=OP2+PQ2

⇒2PQ+1=49

⇒PQ=24cm

∴OQ−PQ=1cm

⇒OQ=(PQ+1)cm=25cm

Now, sinQ=OP/OQ=7/25

and, cosQ=PQ/OQ=24/25