Two arbitllery bases are located at the points A and C represented in the figure each of the bases locates an enemy airplane at point B .the base at A measures the angle of elevation to the airplane to be 95° and the distance between the two bases is 739 meters if the distance between from the base at C to the plane is 2517 meters what is the measure ,in degrees of CBA?
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sɪɴᴄᴇ ᴛʜᴇ ᴍɪᴅ-ᴘᴏɪɴᴛ ᴏғ ᴀʙ ɪs ᴀᴛ ᴛʜᴇ ᴏʀɪɢɪɴ ᴏ ᴀɴᴅ ᴀʙ=2ᴀ
∴ ᴏᴀ=ᴏʙ=ᴀ.
ᴛʜᴜs, ᴛʜᴇ ᴄᴏᴏʀᴅɪɴᴀᴛᴇs ᴏғ ᴀ ᴀɴᴅ ʙ ᴀʀᴇ (ᴀ,0) ᴀɴᴅ (−ᴀ,0) ʀᴇsᴘᴇᴄᴛɪᴠᴇʟʏ.
sɪɴᴄᴇ ᴛʀɪᴀɴɢʟᴇs ᴀʙᴄ. ᴀɴᴅ ᴀʙᴄ' ᴀʀᴇ ᴇǫᴜɪʟᴀᴛᴇʀᴀʟ. ᴛʜᴇʀᴇғᴏʀᴇ, ᴛʜᴇɪʀ ᴛʜɪʀᴅ ᴠᴇʀᴛɪᴄᴇs ᴄ ᴀɴᴅ ᴄ'
ʟɪᴇ ᴏɴ ᴛʜᴇ ᴘᴇʀᴘᴇɴᴅɪᴄᴜʟᴀʀ ʙɪsᴇᴄᴛᴏʀ ᴏғ ʙᴀsᴇ ᴀʙ. ᴄʟᴇᴀʀʟʏ, ʏᴏʏ ɪs ᴛʜᴇ ᴘᴇʀᴘᴇɴᴅɪᴄᴜʟᴀʀ ʙɪsᴇᴄᴛᴏʀ
ᴏғ ᴀʙ. ᴛʜᴜs, ᴄ ᴀɴᴅ ᴄ' ʟɪᴇ ᴏɴ ʏ-ᴀxɪs. ᴄᴏɴsᴇǫᴜᴇɴᴛʟʏ, ᴛʜᴇɪʀ x-ᴄᴏᴏʀᴅɪɴᴀᴛᴇs ᴀʀᴇ ᴇǫᴜᴀʟ ᴛᴏ ᴢᴇʀᴏ.
ɪɴ △ᴀᴏᴄ,ᴡᴇʜᴀᴠᴇ
ᴏᴀ
2
+ᴏᴄ
2
=ᴀᴄ
2
⇒ᴀ
2
+ᴏᴄ
2
=(2ᴀ)
2
⇒ᴏᴄ
2
=4ᴀ
2
−ᴀ
2
⇒ᴏᴄ
2
=3ᴀ
2
ᴏᴄ=
3ᴀ
sɪᴍɪʟᴀʀʟʏ, ʙʏ ᴀᴘᴘʟʏɪɴɢ ᴘʏᴛʜᴀɢᴏʀᴀs ᴛʜᴇᴏʀᴇᴍ ɪɴ △ᴀᴏᴄ; ᴡᴇ ʜᴀᴠᴇ ᴏᴄ
′
=
3ᴀ
ᴛʜᴜs, ᴛʜᴇ ᴄᴏᴏʀᴅɪɴᴀᴛᴇs ᴏғ ᴄ ᴀɴᴅ ᴄ' ᴀʀᴇ (0,
3
ᴀ)ᴀɴᴅ(0,−
3
ᴀ)ʀᴇsᴘᴇᴄᴛɪᴠᴇʟʏ.
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