Math

# Two arbitllery bases are located at the pointsA 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?

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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