Question

1. In triangle ABC, the measure of ∠B is 90°, BC=16, and AC=20. Triangle DEF is similar to triangle ABC, where vertices D, E, and F correspond to vertices A, B, and C, respectively, and each side of triangle DEF is ⅓ the length of the corresponding side of triangle ABC. What is the value of sinF?​

Answer 1

Answer:

ᴀɴꜱᴡᴇʀ ᴇxᴘʟᴀɴᴀᴛɪᴏɴ:

ᴛʀɪᴀɴɢʟᴇ ᴀʙᴄ ɪꜱ ᴀ ʀɪɢʜᴛ ᴛʀɪᴀɴɢʟᴇ ᴡɪᴛʜ ɪᴛꜱ ʀɪɢʜᴛ ᴀɴɢʟᴇ ᴀᴛ ʙ. ᴛʜᴇʀᴇꜰᴏʀᴇ, ᴀᴄ ɪꜱ ᴛʜᴇ ʜʏᴘᴏᴛᴇɴᴜꜱᴇ ᴏꜰ ʀɪɢʜᴛ ᴛʀɪᴀɴɢʟᴇ ᴀʙᴄ, ᴀɴᴅ ᴀʙ ᴀɴᴅ ʙᴄ ᴀʀᴇ ᴛʜᴇ ʟᴇɢꜱ ᴏꜰ ʀɪɢʜᴛ ᴛʀɪᴀɴɢʟᴇ ᴀʙᴄ. ᴀᴄᴄᴏʀᴅɪɴɢ ᴛᴏ ᴛʜᴇ ᴘʏᴛʜᴀɢᴏʀᴇᴀɴ ᴛʜᴇᴏʀᴇᴍ,

ᴀʙ=√202−162=√400−256=√144=12

ꜱɪɴᴄᴇ ᴛʀɪᴀɴɢʟᴇ ᴅᴇꜰ ɪꜱ ꜱɪᴍɪʟᴀʀ ᴛᴏ ᴛʀɪᴀɴɢʟᴇ ᴀʙᴄ, ᴡɪᴛʜ ᴠᴇʀᴛᴇx ꜰ ᴄᴏʀʀᴇꜱᴘᴏɴᴅɪɴɢ ᴛᴏ ᴠᴇʀᴛᴇx ᴄ, ᴛʜᴇ ᴍᴇᴀꜱᴜʀᴇ ᴏꜰ ᴀɴɢʟᴇ∠ꜰ ᴇQᴜᴀʟꜱ ᴛʜᴇ ᴍᴇᴀꜱᴜʀᴇ ᴏꜰ ᴀɴɢʟᴇ∠ᴄ. ᴛʜᴇʀᴇꜰᴏʀᴇ, ꜱɪɴꜰ=ꜱɪɴᴄ. ꜰʀᴏᴍ ᴛʜᴇ ꜱɪᴅᴇ ʟᴇɴɢᴛʜꜱ ᴏꜰ ᴛʀɪᴀɴɢʟᴇ ᴀʙᴄ,

ꜱɪɴꜰ = ᴏᴘᴘᴏꜱɪᴛᴇꜱɪᴅᴇ/ʜʏᴘᴏᴛᴇɴᴜꜱᴇ = ᴀʙ/ᴀᴄ = 12/20 = ⅗

ᴛʜᴇʀᴇꜰᴏʀᴇ, ꜱɪɴꜰ=⅗.

ᴛʜᴇ ꜰɪɴᴀʟ ᴀɴꜱᴡᴇʀ ɪꜱ ⅗ ᴏʀ 0.6.

Answer 2

Answer:

apna muja itna tnx ku diya

Step-by-step explanation:

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